text:
\section{Introduction}
Black holes are among the most extraordinary objects in the Universe.
The direct observations of black holes through the detection of gravitational
waves~\cite{Abbott:2016blz,Abbott:2017oio} and the reconstruction of the black hole
shadow~\cite{Akiyama:2019cqa} have definitely raised them from being exotic solutions
of general relativity, to the status of real astrophysical systems with well determined
characteristics.
\par
The original {\em no-hair\/} conjecture states that black hole solutions should not carry any other
charges~\cite{Ruffini:1971bza} except three fundamental parameters, namely the mass $M$,
angular momentum $J$ and electric charge $Q$~\cite{Hawking:1971vc}.
However, there could exist other charges associated with inner gauge symmetries
(and fields), and it is now known that black holes could also have (soft) quantum
hair~\cite{Hawking:2016msc}.
The {\em general\/} existence of {\em hairy\/} black hole solutions is precisely the topic under
study in this article.
\par
For a long time different scenarios have been studied for circumventing the no-hair theorem
(see Refs.~\cite{Sotiriou:2011dz,Babichev:2013cya,Cisterna:2014nua,Sotiriou:2013qea,
Antoniou:2017acq,Antoniou:2017hxj,Grumiller:2019fmp}
for some recent works and Refs.~\cite{Volkov:1989fi,Kanti:1995vq,Kanti:1997br,Zloshchastiev:2004ny}
for earlier works).
For instance, scalar fields have played a preponderant role, mainly due to their simplicity
and also in analogy with particle physics and cosmology (see also Refs.~\cite{Martinez:2004nb,Herdeiro:2015waa,Sotiriou:2015pka} and references therein).
In this paper, following our previous work~\cite{Ovalle:2018umz}, instead of considering specific
fundamental fields to generate hair in black holes, we shall just assume the presence of a
generic source in addition to the one generating the vacuum Schwarzschild geometry.
We then impose a minimal set of conditions we expect should hold for hairy black holes,
namely:
i) we require that the system has a well-defined event horizon and
ii) the additional source is described by a conserved energy-momentum tensor $\theta_{\mu\nu}$
which satisfies either the strong (SEC) or the dominant energy condition (DEC) in the region outside
the event horizon.
\par
From the technical point of view, we will also assume the energy-momentum tensor $\theta_{\mu\nu}$
is {\em decoupled from the vacuum\/} by means of the extended gravitational decoupling
method (EGD henceforth) of Ref.~\cite{Ovalle:2019qyi}.
This approach was originally introduced in Ref.~\cite{Ovalle:2017fgl} in the form of the so-called
minimal geometric deformation (MGD)~\cite{Ovalle:2007bn,Ovalle:2020fuo}
(for some earlier works on the MGD, see for instance Refs.~\cite{Ovalle:2008se,Ovalle:2010zc,
Casadio:2012pu,Casadio:2012rf,Ovalle:2013vna,Casadio:2013uma,Ovalle:2013xla,
Ovalle:2014uwa,Casadio:2015jva,Casadio:2015gea,Ovalle:2015nfa,Cavalcanti:2016mbe},
and Refs.~\cite{daRocha:2017cxu,daRocha:2017lqj,Fernandes-Silva:2017nec,Casadio:2017sze,
Fernandes-Silva:2018abr,Contreras:2018vph,Contreras:2018gzd,Contreras:2018nfg,
Panotopoulos:2018law,daRocha:2019pla,Heras:2019ibr,Rincon:2019jal,
daRocha:2020rda,Contreras:2020fcj,Arias:2020hwz,daRocha:2020jdj,Tello-Ortiz:2020euy,
daRocha:2020gee,Meert:2020sqv} for some recent applications).
Analogously to the electro-vacuum and scalar-vacuum cases, in this work we will thus consider
a Schwarzschild black hole surrounded by a spherically symmetric ``tensor-vacuum'',
represented by the aforementioned $\theta_{\mu\nu}$.
Following the EGD, we can separate the complete Einstein field equations and
obtain the ``quasi-Einstein" equations for $\theta_{\mu\nu}$
[See Eqs.~\eqref{ec1d}-\eqref{ec3d} below].
These are precisely the equations of motion for the deformed Schwarzschild vacuum,
which after decoupling, contains five unknown functions that can be further analysed
by imposing the two conditions discussed above.
\par
The paper is organised as follows:
in Section~\ref{Sgd}, we first review the fundamentals of the EGD approach
to a spherically symmetric system containing two sources;
in Section~\ref{Shbh}, after imposing a simple condition to guarantee a well defined horizon,
and after considering the strong and dominant energy conditions on $\theta_{\mu\nu}$,
we show a new way to evade the no-hair theorem.
We apply this to generate two new families of hairy black holes containing primary hairs.
As a special case, we show a non-trivial extension
of the Reissner-Nordstr\"om  black hole associated with a non-linear
electrodynamics; finally, we summarize our conclusions in Section~\ref{Scon}.
\section{Gravitational Decoupling}
\label{Sgd}
In this Section, we briefly review the EGD for spherically symmetric gravitational systems
described in detail in Ref.~\cite{Ovalle:2019qyi}. The gravitational decoupling approach and its extended version EGD are particularly attractive for at least three reasons~\cite{Ovalle:2017wqi,
Gabbanelli:2018bhs,Heras:2018cpz,Estrada:2018zbh,Sharif:2018toc,Morales:2018nmq,
Sharif:2018pzr,Morales:2018urp,Estrada:2018vrl,Sharif:2018tiz,Ovalle:2018ans,
Contreras:2019fbk,Maurya:2019wsk,Contreras:2019iwm,Contreras:2019mhf,
Gabbanelli:2019txr,Estrada:2019aeh,Ovalle:2019lbs,Ovalle:2019lbs,Maurya:2019hds,Hensh:2019rtb,Cedeno:2019qkf,Leon:2019abq,Torres:2019mee,
Casadio:2019usg,Singh:2019ktp,Maurya:2019noq,Sharif:2019mjn,Singh:2019ktp,
Abellan:2020wjw,Sharif:2020vvk,Tello-Ortiz:2020ydf,
Maurya:2020rny,Rincon:2020izv,Sharif:2020arn,Maurya:2020gjw}:
a) it allows for extending known (seed) solutions of the Einstein field equations into
more complex ones;
b) it can be used to systematically reduce (decouple) a complex energy-momentum
tensor $T_{\mu\nu}$ into simpler components; and
c) it can be used to find solutions in gravitational theories beyond Einstein's.
In light of the above, it is natural to apply the EGD for the purpose of describing
hairy black holes.
\par
Let us consider the Einstein field equations~\footnote{We use units with $c=1$ and $k^2=8\,\pi\,G_{\rm N}$,
where $G_{\rm N}$ is Newton's constant.}
\begin{equation}
\label{corr2}
G_{\mu\nu}
\equiv
R_{\mu\nu}-\frac{1}{2}\,R\, g_{\mu\nu}
=
k^2\,\tilde{T}_{\mu\nu}
\ ,
\end{equation}
with a total energy-momentum tensor containing two contributions,
\begin{equation}
\label{emt}
\tilde{T}_{\mu\nu}
=
T^{\rm}_{\mu\nu}
+
\theta_{\mu\nu}
\ ,
\end{equation}
where $T_{\mu\nu}$ is usually associated with some known solution of general relativity,
whereas $\theta_{\mu\nu}$ may contain new fields or a new gravitational sector.
Since the Einstein tensor $G_{\mu\nu}$ satisfies the Bianchi identity, the total source must be
covariantly conserved,
\begin{equation}
\nabla_\mu\,\tilde{T}^{\mu\nu}=0
\ .
\label{dT0}
\end{equation}
For spherically symmetric and static systems, the metric $g_{\mu\nu}$ can be written as
\begin{equation}
ds^{2}
=
e^{\nu (r)}\,dt^{2}-e^{\lambda (r)}\,dr^{2}
-r^{2}\,d\Omega^2
\ ,
\label{metric}
\end{equation}
where $\nu =\nu (r)$ and $\lambda =\lambda (r)$ are functions of the areal
radius $r$ only and $d\Omega^2=d\theta^{2}+\sin ^{2}\theta \,d\phi ^{2}$.
The Einstein equations~(\ref{corr2}) then read
\begin{eqnarray}
\label{ec1}
k^2\!
\left(
T_0^{\ 0}+\theta_0^{\ 0}
\right)
&=&
\frac 1{r^2}
-
e^{-\lambda }\left( \frac1{r^2}-\frac{\lambda'}r\right)
\\
\label{ec2}
k^2\!
\left(T_1^{\ 1}+\theta_1^{\ 1}\right)
&=&
\frac 1{r^2}
-
e^{-\lambda }\left( \frac 1{r^2}+\frac{\nu'}r\right)
\\
\label{ec3}
k^2\!
\left(T_2^{\ 2}+\theta_2^{\ 2}\right)
&=&
-\frac {e^{-\lambda }}{4}
\left(2\nu''+\nu'^2-\lambda'\nu'
+2\,\frac{\nu'-\lambda'}r\right)
\ ,
\end{eqnarray}
where $f'\equiv \partial_r f$ and $\tilde{T}_3^{{\ 3}}=\tilde{T}_2^{\ 2}$ due to the spherical symmetry.
By simple inspection, we can identify in Eqs.~\eqref{ec1}-\eqref{ec3} an effective density
\begin{equation}
\tilde{\rho}
=
T_0^{\ 0}
+
\theta_0^{\ 0}
\ ,
\label{efecden}
\end{equation}
an effective radial pressure
\begin{equation}
\tilde{p}_{r}
=
-T_1^{\ 1}
-\theta_1^{\ 1}
\ ,
\label{efecprera}
\end{equation}
and an effective tangential pressure
\begin{equation}
\tilde{p}_{t}
=
-T_2^{\ 2}
-\theta_2^{\ 2}
\ .
\label{efecpretan}
\end{equation}
Moreover, the anisotropy
\begin{equation}
\label{anisotropy}
\Pi
\equiv
\tilde{p}_{t}-\tilde{p}_{r}
\end{equation}
usually does not vanish and the system of Eqs.~(\ref{ec1})-(\ref{ec3}) may be
treated as an anisotropic fluid~\cite{Herrera:1997plx,Mak:2001eb}.
\par
We next consider a solution to the Eqs.~\eqref{corr2} for the seed source $T_{\mu\nu}$
alone [that is, $\theta_{\mu\nu}=0$], which we write as
\begin{equation}
ds^{2}
=
e^{\xi (r)}\,dt^{2}
-e^{\mu (r)}\,dr^{2}
-
r^{2}\,d\Omega^2
\ ,
\label{pfmetric}
\end{equation}
where
\begin{equation}
\label{standardGR}
e^{-\mu(r)}
\equiv
1-\frac{k^2}{r}\int_0^r x^2\,T_0^{\, 0}(x)\, dx
=
1-\frac{2\,m(r)}{r}
\end{equation}
is the standard general relativity expression containing the Misner-Sharp mass function $m=m(r)$.
The addition of the source $\theta_{\mu\nu}$ can then be accounted for by the extended
geometric deformation (EGD) of the seed metric~\eqref{pfmetric}, namely
\begin{eqnarray}
\label{gd1}
\xi
&\rightarrow &
\nu\,=\,\xi+\alpha\,g
\\
\label{gd2}
e^{-\mu}
&\rightarrow &
e^{-\lambda}=e^{-\mu}+\alpha\,f
\ ,
\end{eqnarray}
where $f$ and $g$ are respectively the geometric deformations for the radial and temporal metric
components, with the parameter $\alpha$ introduced to keep track of these deformations.
By means of Eqs.~(\ref{gd1}) and (\ref{gd2}), the Einstein equations~(\ref{ec1})-(\ref{ec3})
are separated in two sets:
A) one is given by the standard Einstein field equations with the energy-momentum tensor $T_{\mu\nu}$,
that is
\begin{eqnarray}
\label{ec1pf}
&&
k^2\,T_0^{\, 0}
=\frac 1{r^2}
-
e^{-\mu }\left( \frac1{r^2}-\frac{\mu'}r\right)\ ,
\\
&&
\label{ec2pf}
k^2
\,T_1^{\, 1}
=
\frac 1{r^2}
-
e^{-\mu}\left( \frac 1{r^2}+\frac{\xi'}r\right)\ ,
\\
&&
\label{ec3pf}
k^2
\strut\displaystyle
\,T_2^{\, 2}
=
-\frac {e^{-\mu }}{4}
\left(2\xi''+\xi'^2-\mu'\xi'
+2\,\frac{\xi'-\mu'}r\right)
\ ,
\end{eqnarray}
which is assumed to be solved by the seed metric~(\ref{pfmetric});
B) the second set contains the source $\theta_{\mu\nu}$ and reads
\begin{eqnarray}
\label{ec1d}
k^2\,\theta_0^{\ 0}
&=&
-\alpha\,\frac{f}{r^2}
-\alpha\,\frac{f'}{r}\ ,
\\
\label{ec2d}
k^2\,\theta_1^{\ 1}
+\alpha\,Z_1
&=&
-\alpha\,f\left(\frac{1}{r^2}+\frac{\nu'}{r}\right)
\\
\label{ec3d}
k^2\,\theta_2^{\ 2}
+\alpha\,Z_2
&=&
-\alpha\,\frac{f}{4}\left(2\,\nu''+\nu'^2+2\frac{\nu'}{r}\right)
\nonumber
\\
&&
-\alpha\,\frac{f'}{4}\left(\nu'+\frac{2}{r}\right)
\ ,
\end{eqnarray}
where
\begin{eqnarray}
\label{Z1}
Z_1
&=&
\frac{e^{-\mu}\,g'}{r}
\\
\label{Z2}
4\,Z_2&=&e^{-\mu}\left(2g''+g'^2+\frac{2\,g'}{r}+2\xi'\,g'-\mu'g'\right)
\ .
\end{eqnarray}
The above equations clearly show that the tensor $\theta_{\mu\nu}$ must vanish
when the deformations vanish ($\alpha=0$).
Moreover, on assuming $g=0$, Eqs.~\eqref{ec1d}-\eqref{ec3d} reduce to the simpler
``quasi-Einstein" system of the MGD of Ref.~\cite{Ovalle:2017fgl},
in which $f$ is only determined by $\theta_{\mu\nu}$ and the undeformed metric~\eqref{pfmetric}.
\par
It is also important to discuss the conservation equation~\eqref{dT0} which now reads
\begin{eqnarray}
\label{con111}
&&
\left({T}_1^{\ 1}\right)'
-
\frac{\xi'}{2}\left({T}_0^{\ 0}-{T}_1^{\ 1}\right)
-
\frac{2}{r}\left({T}_2^{\ 2}-{T}_1^{\ 1}\right)
\nonumber
\\
&&
-\frac{\alpha\,g'}{2}\left({T}_0^{\ 0}-{T}_1^{\ 1}\right)
\nonumber
\\
&&
+\left({\theta}_1^{\ 1}\right)'
-
\frac{\nu'}{2}\left({\theta}_0^{\ 0}-{\theta}_1^{\ 1}\right)
-
\frac{2}{r}\left({\theta}_2^{\ 2}-{\theta}_1^{\ 1}\right)
=
0
\ .
\quad
\end{eqnarray}
The first line precisely represents the divergence of $T_{\mu\nu}$ computed with the
covariant derivative $\nabla^{(\xi,\mu)}$ for the metric~(\ref{pfmetric}),
and is a linear combination of the Einstein field equations~\eqref{ec1pf}-\eqref{ec3pf}.
In fact, the Einstein tensor ${G}_{\mu\nu}$ for the metric~(\ref{pfmetric}) must satisfy its respective
Bianchi identity, and the energy momentum tensor $T_{\mu \nu }$ is therefore conserved
by construction in this geometry,
\begin{equation}
\label{pfcon}
\nabla^{(\xi,\mu)}_\sigma\,T^{\sigma}_{\ \nu}=0
\ ,
\end{equation}
Upon using the deformed metric in Eq.~\eqref{metric}, one instead obtains
\begin{equation}
\label{divs}
\nabla_\sigma\,T^{\sigma}_{\ \nu}
=
\nabla^{(\xi,\mu)}_\sigma\,T^{\sigma}_{\ \nu}
-
\alpha\,\frac{g'}{2}\left({T}_0^{\ 0}-{T}_1^{\ 1}\right)\delta^1_\nu
\ ,
\end{equation}
which explains the origin of the term in the second line of Eq.~\eqref{con111}.
Finally, Eq.~\eqref{con111} becomes
\begin{eqnarray}
\label{con22}
0
&=&
\nabla_\sigma\,T^{\sigma}_{\ \nu}
+\nabla_\sigma\theta^{\sigma}_{\ \nu}
\nonumber
\\
&=&
\alpha\,\frac{g'}{2}\left({T}_0^{\ 0}-{T}_1^{\ 1}\right)\delta^1_\nu
+
\nabla_\sigma\theta^{\sigma}_{\ \nu}
\nonumber
\\
&=&
\left({\theta}_1^{\ 1}\right)'
-
\frac{\nu'}{2}\left({\theta}_0^{\ 0}-{\theta}_1^{\ 1}\right)
-
\frac{2}{r}\left({\theta}_2^{\ 2}-{\theta}_1^{\ 1}\right)
\nonumber
\\
&&
-
\alpha\,\frac{g'}{2}\left({T}_0^{\ 0}-{T}_1^{\ 1}\right)
\ ,
\end{eqnarray}
which is also a linear combination of the ``quasi-Einstein'' field equations~\eqref{ec1d}-\eqref{ec3d}
for the source $\theta_{\mu\nu}$.
We therefore conclude that the two sources $T_{\mu\nu}$ and $\theta_{\mu\nu}$ can be successfully decoupled
by means of the EGD.
This result is particularly remarkable, since it does not require a perturbative expansion in the parameter
$\alpha$~\cite{Ovalle:2020fuo}.
\section{Hairy black holes}
\label{Shbh}
Conditions to evade the no-hair theorem have been investigated for a long time~\cite{Sotiriou:2011dz,Babichev:2013cya,Cisterna:2014nua,Sotiriou:2013qea,
	Antoniou:2017acq,Antoniou:2017hxj,Grumiller:2019fmp,Volkov:1989fi,Kanti:1995vq,Kanti:1997br,Zloshchastiev:2004ny}. A straightforward possibility is to fill the static vacuum with some source of potentially fundamental origin,
often described as a scalar field~\cite{Martinez:2004nb,Herdeiro:2015waa,Sotiriou:2015pka}.
We recently considered a more general scenario within the MGD approach,
where the Schwarzschild vacuum for $T_{\mu\nu}=0$ is filled with a generic static and
spherically symmetric source of energy-momentum tensor $\theta_{\mu\nu}$,
namely, a ``tensor-vacuum''~\cite{Ovalle:2018umz}.
This leads to hairy black hole solutions with a rich geometry described by the mass $M$ and
a discrete set of charges generating primary hair.
However, the MGD~\eqref{gd2} leaves the temporal component of the metric~\eqref{metric}
exactly equal to the Schwarzschild one,
\begin{equation}
e^\nu
=
e^\xi
=
1-\frac{2\,M}{r}
\ ,
\label{schwR}
\end{equation}
which hinders the existence of stable black holes with a well-defined event horizon.
Indeed, the relation~\eqref{schwR} implies that only hairy black hole solutions
with the event horizon at $r_{\rm H} = 2\,M$ can be free of pathologies.
The advantage of the EGD is that the temporal component is also modified
according to Eq.~\eqref{gd1}, thus yielding a potentially larger number of hairy black
hole solutions with horizons other than $r_{\rm H} = 2\,M$.
\par
We apply the analysis in the previous Section to the particular case of $T_{\mu\nu}=0$.
The seed metric~\eqref{pfmetric} is thus given by the Schwarzschild solution with
\begin{equation}
e^\xi
=
e^{-\mu}
=
1-\frac{2\,M}{r}
\ ,
\label{schw}
\end{equation}
which solves Eqs.~\eqref{ec1pf}-\eqref{ec3pf} for $T_{\mu\nu}=0$.
In order to find hairy black holes, we then need to solve the resulting
``quasi-Einstein'' system~\eqref{ec1d}-\eqref{ec3d}, which contain the three components
of $\theta_{\mu\nu}$ and the two deformations $f$ and $g$.
Furthermore, we reduce the number of unknown quantities, so that they specify
a unique solution, by prescribing the two conditions discussed in the Introduction.
\par
First of all, in order to have black hole solutions with a well-defined horizon structure,
we demand that the deformed metric~\eqref{metric} satisfies~\footnote{We remark that
Eq.~\eqref{constr1} implies the condition~\eqref{cRh} but is not necessary for it to hold,
as one could also consider cases with $e^{\nu}\not= e^{-\lambda}$ for $r\not=r_{\rm H}$.}
\begin{equation}
\label{constr1}
e^{\nu}=e^{-\lambda}
\ .
\end{equation}
This condition ensures that the radius $r=r_{\rm H}$ such that
\begin{equation}
\label{cRh}
e^{\nu(r_{\rm H})}=e^{-\lambda(r_{\rm H})}=0
\end{equation}
will be both a killing horizon ($e^{\nu}=0$) and a causal horizon $(e^{-\lambda}=0)$.
A direct consequence of the condition~\eqref{constr1}, following from the Einstein
equations~\eqref{ec1} and~\eqref{ec2}, is the equation of state
\begin{equation}
\tilde{p}_{r}
=
-\tilde{\rho}
\ .
\label{schwcon}
\end{equation}
Therefore, only negative radial pressure is allowed (for positive density).
The condition~\eqref{constr1} and the Schwarzschild solution~\eqref{schw} then relate the
metric deformations $f$ and $g$ according to
\begin{equation}
\label{fg}
\alpha\,f(r)
=
\left(1-\frac{2\,M}{r}\right)\left(e^{\alpha\,g(r)}-1\right)
\ ,
\end{equation}
so that the line element~\eqref{metric} becomes
\begin{eqnarray}
\label{hairyBH}
ds^{2}
&=&
\left(1-\frac{2\,M}{r}\right)
e^{\alpha\,g(r)}
dt^{2}
-\left(1-\frac{2\,M}{r}\right)^{-1}
e^{-\alpha\,g(r)}
dr^2
\nonumber
\\
&&
-r^{2}\,d\Omega^2
\ .
\end{eqnarray}
\par
We are now left with the deformation $g$ and the three components of $\theta_{\mu\nu}$,
which must satisfy the three ``quasi-Einstein'' Eqs.~\eqref{ec1d}-\eqref{ec3d}.
We can therefore impose some physically motivated restriction on $g$ or a constraint on
$\theta_{\mu\nu}$, like a reasonable equation of state.
For instance, in the region $r\geq\,2\,M$, we can consider the tensor-vacuum satisfies
\begin{equation}
\label{generic}
\theta_0^{\,0}
=
a\,\theta_1^{\,1}+b\,\theta_2^{\,2}
\ ,
\end{equation}
with $a$ and $b$ constants.
In this case, Eqs.~(\ref{ec1d})-(\ref{ec3d}) yield the differential equation
\begin{eqnarray}
\label{master}
&&b\,r\,(r-2\,M)\,h''+2\,\left[(a+b-1)\,r-2\,(a-1)\,M\right]
h'
\nonumber
\\
&&
+2\,(a-1)\,h=2\,(a-1)
\ ,
\end{eqnarray}
for
\begin{equation}
h(r)
=
e^{\alpha\,g(r)}
\ .
\label{h}
\end{equation}
The solution can be written as
\begin{equation}
\label{master2}
e^{\alpha\,g(r)}
=
1+\frac{1}{r-2\,M}
\left[\ell_0+r\left(\frac{\ell}{r}\right)^{2(1-a)/b}
\right]
\ ,
\end{equation}
where $\ell_0$ and $\ell$ are constants (proportional to $\alpha$) with dimensions of a length.
By using this expression in the line element~\eqref{hairyBH},
we obtain the metric functions
\begin{equation}
\label{bh}
e^{\nu}
=
e^{-\lambda}
=
1-\frac{2\,{\cal M}}{r}
+
\frac{{\ell}^n}{r^n}
\ ,
\end{equation}
where we defined the new mass as ${\cal M}=M+\ell_0/2$ and
\begin{equation}
\label{n}
n
=
\frac{2}{b}
\left(a-1\right)
\ ,
\end{equation}
with $n>1$ for a correct asymptotic behavior.~\footnote{Note that a trivial deformation
which leaves the Schwarzschild metric~\eqref{schw} unaffected is also recovered by
setting $a=1$ ($n=0$) in Eq.~\eqref{master}.
We will have more to say about this in the next subsections.}
The possible horizons $r=r_{\rm H}$ are given by the solutions of
\begin{equation}
\label{horizon}
r_{\rm H}^n-2\,{\cal M}\,r_{\rm H}^{n-1}+\ell = 0
\ ,
\end{equation}
and the space-time represents a Kiselev black hole~\cite{Kiselev:2002dx},
which was analyzed in great detail by Visser in Ref.~\cite{Visser:2019brz}.
This line element is produced by the effective density
\begin{equation}
\tilde{\rho}
=
\theta_0^{\ 0}
=
\alpha\,\frac{(n-1)\,\ell^n}{k^2\,r^{n+2}}
\ ,
\label{efecdenx}
\end{equation}
the effective radial pressure
\begin{equation}
\tilde{p}_{r}
=
-\theta_1^{\ 1}
=
-\tilde{\rho}
\ ,
\label{efecprax}
\end{equation}
and the effective tangential pressure
\begin{equation}
\tilde{p}_{t}
=
-\theta_2^{\ 2}
=
\frac{n}{2}\,\tilde{\rho}
\ .
\label{efecptanx}
\end{equation}
The anisotropy~\eqref{anisotropy} is thus given by
\begin{equation}
\Pi
=
\left(\frac{n}{2}+1\right)\,\tilde{\rho}
\ .
\end{equation}
We see that the Schwarzschild-de~Siter solution ($n=-2$) is the only one which allows
for an isotropic tensor-vacuum.
On the other hand, the DEC, namley $\tilde{\rho}\geq |\tilde{p}_r|$ and
$\tilde{\rho}\geq|\tilde{p}_t|$, yields $n\le2$.
Combining this with asymptotic flatness ($n>1$), we obtain the range
\begin{equation}
\label{n}
1
\le
n
\le
2
\ .
\end{equation}
The extreme cases $n=1$ and $n=2$ are, respectively, the Schwarzschild solution and the
conformal solution with traceless $\theta_{\mu\nu}$, like the Maxwell case.
Since the Kiselev black hole has already been studied extensively, we will abandon Eq.~\eqref{generic}
and continue analysing the deformed metric~\eqref{hairyBH} based on energy conditions.
\par
Let us recall that the energy conditions are a set of requirements which are usually imposed
on the energy-momentum tensor to avoid exotic matter sources, hence we can see them
as sensible guidelines to avoid classically unphysical configurations~\cite{Visser:1995cc,Curiel:2014zba}.
In particular, we will impose energy conditions on the source $\theta_{\mu\nu}$ in the
region of space-time accessible to an outer observer (while possibly relax them
inside the event horizon).
\subsection{Strong energy condition}
\label{SSsec}
Let us start with the SEC, namely
\begin{eqnarray}
\nonumber
&&
\tilde{\rho}+\tilde{p}_r+2\,\tilde{p}_t
\geq
0
\\
\label{strong01}
&&
\tilde{\rho}+\tilde{p}_r
\geq
0
\\
&&
\tilde{\rho}+\tilde{p}_t
\geq
0
\ ,
\nonumber
\end{eqnarray}
which, as a consequence of Eq.~\eqref{schwcon}, reduce to
\begin{eqnarray}
\label{strong2}
\theta_2^{\ 2}
&\leq&
0
\\
\theta_0^{\ 0}
&\geq&
\theta_2^{\ 2}
\ ,
\label{strong3}
\end{eqnarray}
where we used the definitions~\eqref{efecden} and~\eqref{efecpretan}.
\par
Using Eqs.~\eqref{ec1d} and~\eqref{ec3d} we find that the conditions~\eqref{strong2}
and~\eqref{strong3} respectively lead to the second-order linear differential inequalities
\begin{eqnarray}
\label{strong5}
&&G_1(r)\equiv
{(r-2\,M) \,h''+2\,h'}
\geq
0\ ,\\
\label{strong51}
&&G_2(r)
\equiv
r\,(r-2\,M)\,h''
+4\,M\,h'
-2\,h+2
\geq
0\ ,
\end{eqnarray}
where $h$ was defined in Eq.~\eqref{h}.
It is now useful to recall that a Gr\"{o}nwall's inequality of the form
\begin{equation}
\label{gro1}
U'(r)\leq\,\beta(r)\,U(r)
\ ,
\end{equation}
in the interval $r_0\leq\,r\,\leq\,\infty$, admits the solution
\begin{equation}
\label{gro2}
U(r)
\leq
U(r_0)\,
e^{\int_{r_0}^{r}\beta(s)\,ds}
\equiv
U_0(r)
\ ,
\end{equation}
where the bounding function $U_0$ is obtained by saturating the differential inequality~\eqref{gro1}.
For the inequality~\eqref{strong5}, we can define
\begin{equation}
U(r)=-h'(r)
\end{equation}
and $\beta(r)=-2\,(r-2\,M)^{-1}$, so that Eq.~\eqref{gro2} yields
\begin{equation}
h'(r)\geq\,h'(r_0)\left(\frac{r_0-2\,M}{r-2\,M}\right)^2
\ ,
\end{equation}
and finally
\begin{equation}
h(r)
\geq
h(r_0)
+
(r_0-2\,M)
\left(1-\frac{r_0-2\,M}{r-2\,M}\right)
h'(r_0)
\ .
\end{equation}
We therefore find that the bounding function solving $G_1(r)=0$ behaves as
\begin{equation}
\label{beh}
h_1(r)
\sim
c_1-\frac{\ell_1}{r-2\,M}
\ ,
\end{equation}
where $c_1$ is a dimensionless constants and $\ell_1$ a constant with dimensions of a length.
However, any deformation of the form in Eq.~\eqref{beh} plugged into the metric~\eqref{hairyBH}
uniquely leads to
\begin{equation}
e^\nu
=
e^{-\lambda}
=
c_1
\left(
1
-\frac{2\,c_1\,M+\ell_1}{c_1\,r}
\right)
\ ,
\end{equation}
which becomes the Schwarzschild solution~\eqref{schw} by imposing asymptotic flatness
(that is, setting $c_1=1$) and rescaling the mass $2\,M+\ell_1\to 2\,M$.
Indeed, we notice that $G_1(r)=0$ equals the differential equation~\eqref{master} for $a=1$,
whose solution yields the Schwarzschild metric.
On the other hand, following the same procedure for the inequality~\eqref{strong51},
we find that the bounding function satisfying $G_2(r)=0$ behaves as
\begin{equation}
\label{beh2}
h_2(r)
\sim
1-\frac{1}{r-2\,M}
\left(\ell_2
-\frac{\Lambda}{3}\,{r^3}
\right)
\ ,
\end{equation}
where $\ell_2$ is again a length and $\Lambda$ a constant with dimensions of the inverse
of a squared length.
Likewise, the deformation~\eqref{beh2} plugged into the metric~\eqref{hairyBH} leads to
\begin{equation}
e^\nu
=
e^{-\lambda}
=
1
-\frac{2\,M+\ell_2}{r}+\frac{\Lambda}{3}\,r^2
\ ,
\end{equation}
which is the Schwarzschild-de~Sitter metric with cosmological constant $\Lambda$ and mass
$2\,M+\ell_2\to 2\,M$.
Again, notice that $G_2(r)=0$ is the differential equation~\eqref{master} for $a=0$ and $b=1$
and the bounding solution $h_2$ for the extremal case $G_2(r)=0$ (with $\alpha\neq 0$) leads
to the line element~\eqref{bh} with $n=-2$.
Since both inequalities~\eqref{strong5} and~\eqref{strong51} must hold, the unique bounding
deformation $h_0(r)$ which solves $G_1(r)=G_2(r)=0$ is obtained when Eq.~\eqref{beh}
equals Eq.~\eqref{beh2}, that is for $\Lambda=0$.
We thus conclude that the bounding deformations which saturate the SEC are of the form
\begin{equation}
h_0(r)
=
1
-\frac{\ell_0}{r-2\,M}
\label{h0sec}
\end{equation}
and leave the Schwarzschild geometry unaffected.
This is not at all surprising since $G_1(r)=G_2(r)=0$ is tantamount to
$\tilde\rho=\tilde p_r=\tilde p_t=0$ and the Schwarzschild geometry cannot possibly be
deformed in this case.
\par
Before we proceed to consider deformations which do not saturate the inequalities~\eqref{strong5}
and~\eqref{strong51}, we notice that the transformation
\begin{equation}
\label{gauge}
h(r)
\to
\bar h(r)
\equiv
h(r)-\frac{\ell_0}{r-2\,M}
\end{equation}
leaves $G_1(r)$ and $G_2(r)$ invariant.
Under this transformation, the metric functions change as
\begin{equation}
\label{hgauge}
e^\nu
=
e^{-\lambda}
=
\left(1-\frac{2\,M}{r}\right)
h(r)
\to
\left(1-\frac{2\,M}{r}\right)
h(r)
-
\frac{\ell_0}{r}
\ ,
\end{equation}
where it is reasonable to assume that $h(r)$ admits an expansion in powers of $1/r$ for
a regular exterior.
In particular, the effect of the metric transformation~\eqref{hgauge} will amount to
the usual shift of the mass $M\to{\cal M}=M+\ell_0/2$ at order $1/r$.
This redefinition of the asymptotic mass, in turn, will introduce a new dependence on the length
$\ell_0$ in $h(r)$ whenever the latter contains the unshifted seed mass $M={\cal M}-\ell_0/2$,
thus generating a new solution with parameters ${\cal M}$ and $\ell_0$.
Of course, for $h(r)\sim 1$, Eq.~\eqref{gauge} acts like a ``gauge'' symmetry
corresponding to the trivial deformations~\eqref{h0sec} of the seed Schwarzschild
geometry~\eqref{schw}.
\par
We have just seen that the parameter $\ell_0$ in Eq.~\eqref{gauge} appears as a
new ``gauge'' charge.
The way this all works can be made more explicit by considering concrete examples.
Since we are interested in solutions with a proper horizon at $r=r_{\rm H}\sim 2\,M$, which also
behave approximately like the Schwarzschild metric for $r\gg 2\,M$ (so as to meet all experimental
bounds in the weak field regime), we could consider any positive function $G_1(r)$ satisfying the
boundary conditions
\begin{equation}
\label{condition1}
G_1(r)=0
\qquad
{\rm for}
\quad
\left\{
\begin{array}{ll}
r\sim
2\,M
\\
\\
r
\gg
M
\ ,
\end{array}
\right.
\end{equation}
A simple example of such a function containing just the parameters $\alpha$ and $M$ is given by
\begin{equation}
\label{G}
G_{\alpha,M}(r)
=
\frac{\alpha}{M^2}\,(r-2\,M)\,e^{-{r}/{M}}
\ .
\end{equation}
Upon solving Eq.~\eqref{strong5} for the corresponding deformation $h$, we obtain
\begin{equation}
\label{strongg}
h(r)
=
c_1
-
\alpha\,\frac{\ell-r\,e^{-r/M}}{r-2\,M}
\ ,
\end{equation}
where $\alpha\,\ell=\ell_0$ and we can set $c_1=1$ to recover the proper limit for $\alpha=0$
(in which $G_{\alpha,M}\to 0$).
The deformation in Eq.~\eqref{strongg} must also satisfy the inequality~\eqref{strong51},
which becomes
\begin{equation}
\label{Gg}
\frac{\alpha}{M^2}
\left(r^2-2\,M^2\right)
e^{-{r}/{M}}
\geq
0
\ ,
\end{equation}
and it is satisfied for all $r\geq\,\sqrt{2}\,M$.
\par
Finally, using~\eqref{strongg} in the line element~\eqref{hairyBH} yields the metric functions
\begin{equation}
\label{strongBH}
e^{\nu}
=
e^{-\lambda}
=
1-\frac{2\,{\cal M}}{r}+\alpha\,e^{-r/({\cal M}-\alpha\,\ell/2)}
\ ,
\end{equation}
where we modded out the term proportional to $\ell$, corresponding to the gauge
transformation~\eqref{gauge}, by introducing the mass ${\cal M}=M+\alpha\,\ell/2$.
The new solution~\eqref{strongBH} thus asymptotically approaches the Schwarzschild
geometry with a total mass ${\cal M}$.
The source $\theta_{\mu\nu}$ decays exponentially away from the center of the system,
as can be seen from the effective density
\begin{equation}
\tilde{\rho}
=
\theta_0^{\ 0}
=
-\tilde{p}_r
=
\frac{\alpha\,e^{-r/M}}{k^2\,M\,r^2}\left(r-M\right)
\ ,
\label{denstrong}
\end{equation}
and the effective tangential pressure
\begin{equation}
\tilde{p}_{t}
=
-\theta_2^{\ 2}
=
\frac{\alpha\,e^{-r/M}}{2\,k^2\,M^2\,r}\left(r-2\,M\right)
\ .
\label{prestrong}
\end{equation}
We can immediately see some important features of the metric~\eqref{strongBH}.
The first one is that the physical singularity at $r=0$ remains and is further reflected
in the singular behaviour of the effective quantities in Eqs.~\eqref{denstrong}
and~\eqref{prestrong}.
The second feature is that the SEC~\eqref{strong2}
is only satisfied as long as $r\geq 2\,M$, as we can see from~\eqref{prestrong}.
Also notice that in the limit $M\to 0$ the source $\theta_{\mu}^{\ \nu}\to 0$ for $r>0$,
and ${\cal M}\to \alpha\,\ell$.
In other words, the source $\theta_{\mu}^{\ \nu}$ approaches a Dirac-delta function
for vanishing seed mass $M$.
\begin{figure}[t]
\center
\includegraphics[width=8cm]{strong1.pdf}
\\
\caption{Metric function for different values of $\ell$ with $\alpha=0.4$
and $M=1$.
The shift of the horizon $r_{\rm H}$ is controlled by the parameter $\ell$. The Schwarzschild horizon corresponds to the saturated case of the inequality~\eqref{lineq}.}
\label{fig1}
\end{figure}
\begin{figure}[t]
\center
\includegraphics[width=8cm]{strong2.pdf}
\\
\caption{Effective source terms $\times\,10^{4}$ for $\alpha=0.2$.
The horizon is located at $r_{\rm H}\gtrsim\,2\,M$, with $M=1$. }
\label{fig2}
\end{figure}
\par
The equation determining the horizon $r=r_{\rm H}$ of the metric~\eqref{strongBH}
is given by
\begin{equation}
\label{stronghorizon}
\alpha\,\ell
=
r_{\rm H}-2\,M+\alpha\,r_{\rm H}\,e^{-r_{\rm H}/M}
\ ,
\end{equation}
which allows to write the metric~\eqref{strongBH} in terms of its horizon in the form
\begin{eqnarray}
\label{strongBH3}
e^{\nu}
=
e^{-\lambda}
=
1-\frac{\,r_{\rm H}}{r}+\alpha\,\left(e^{-r/M}-\frac{\,r_{\rm H}}{r}\,e^{-r_{\rm H}/M}\right)
\ .
\quad
\end{eqnarray}
It is of course impossible to find analytical solutions to Eq.~\eqref{stronghorizon},
except for particular values of the parameters.
For example, according to our prescription for the SEC, we need
$r_{\rm H}\geq 2\,M$, or
\begin{equation}
\label{lineq}
\ell
\geq
2\,M/e^{2}
\ .
\end{equation}
The extremal case $\ell=2\,M/e^{2}$ leads to the solution
\begin{eqnarray}
\label{strongh2M}
e^{\nu}
=
e^{-\lambda}
=
1-\frac{2\,M}{r}+\alpha\,\left(e^{-r/M}-\frac{2\,M}{e^2\,r}\right)
\ .
\end{eqnarray}
which has the horizon at $r_{\rm H} = 2\,{M}$.
The SEC~\eqref{strong2} and~\eqref{strong3} are both satisfied
in the outer region, but the black hole should have the same thermodynamic properties
of the Schwarzschild geometry.
\par
The metric function~\eqref{strongBH} is plotted in Fig.~\ref{fig1} for a given value of $\alpha$,
which shows that the horizon is shifted to larger radii when $\ell$ increases from the minimum
allowed value~\eqref{lineq} corresponding to $r_{\rm H} = 2\,{M}$.
We find the same behavior when $\alpha$ increases.
In this respect, we notice that the effective density ${\tilde \rho}$ and pressures
${\tilde p}_r$ and ${\tilde p}_t$ in Eqs.~\eqref{denstrong} and~\eqref{prestrong} do not
depend on the parameter $\ell$, unlike the horizon.
This allows us to choose suitable values for the parameters $\alpha$ and $\ell$ such that
the SEC is satisfied for $r\gtrsim r_{\rm H}$, as is shown in Fig.~\ref{fig2},
where both the density and tangential pressure are positive.
We conclude that the metric~\eqref{strongBH} represents a hairy black hole
(having in general non-trivial thermodynamic properties) endowed with the parameters
$\{M,\alpha,\ell\}$, where $\ell_0=\alpha\,\ell$ represents a charge associated with
primary hair.
\subsection{Dominant energy condition}
\label{SSdec}
We shall next consider the DEC, which requires~\cite{Visser:1995cc}
\begin{eqnarray}
\tilde{\rho}
&\geq&
|\tilde{p}_r|
\label{dom1}
\\
\tilde{\rho}
&\geq&
|\tilde{p}_t|
\ .
\label{dom2}
\end{eqnarray}
In particular, we will see that these conditions allow for deforming the Schwarzschild
solution into the Reissner-Nordstr\"{o}m-de~Sitter geometry with an effective charge $Q$
and an effective cosmological constant $\Lambda$.
\par
We first point out that the inequality~\eqref{dom1} is saturated as a consequence
of Eq.~\eqref{schwcon} for a positive effective density, for which Eq.~\eqref{dom2}
reduces to
\begin{equation}
\label{dom3}
-\tilde{\rho}
\le
\tilde{p}_t
\le
\tilde{\rho}
\ .
\end{equation}
We can again write the condition~\eqref{dom3} in terms of the
definitions~\eqref{efecden} and~\eqref{efecpretan} as
\begin{eqnarray}
\label{dom4}
&&
\theta_0^{\ 0}+\,\theta_2^{\ 2}
\geq
0
\\
\label{dom41}
&&
\theta_0^{\ 0}-\,\theta_2^{\ 2}
\geq
0
\ ,
\end{eqnarray}
which yield respectively the differential inequalities
\begin{eqnarray}
\label{dom6}
&&H_1(r)
\equiv
-r(r-2\,M)h''
-4(r-M)h'
-2h+2
\geq
0
\qquad
\\
\label{dom61}
&&H_2(r)
\equiv
r\,(r-2\,M)\,h''
+4\,M\,h'
-2\,h+2
\geq
0
\ ,
\end{eqnarray}
where we used Eqs.~\eqref{ec1d} and~\eqref{ec3d}, and $h$ is the same defined in Eq.~\eqref{h}.
\par
We can then notice that $H_1(r)=0$ is the differential equation~\eqref{master} for $a=0$ and $b=-1$.
Hence, the bounding solution $h_1$ for the extremal case $H_1(r)=0$ (with $\alpha\neq\,0$) leads
to the line element~\eqref{bh} with $n=2$, namely, the Reissner-Nordstr\"om solution
(with an effective charge $Q\sim\ell$).
On the other hand, $H_2(r)=0$ is the differential equation~\eqref{master} for $a=0$ and $b=1$.
Hence, the bounding solution $h_2$ for the extremal case $H_2(r)=0$ leads
to the line element in~\eqref{bh} with $n=-2$, namely, the Schwarzschild-de~Sitter solution with
cosmological constant $\Lambda\sim\ell^{-2}$.
Since $H_1(r)=H_2(r)=0$ corresponds to vanishing $\theta_{\mu\nu}$ like for the SEC,
the unique bounding deformation $h_0(r)=h_1(r)=h_2(r)$ is obtained for $Q=\Lambda=0$,
so that the only possible deformation remains again the trivial one in Eq.~\eqref{h0sec},
which yields the seed Schwarzschild solution.
Indeed, the functions $H_1(r)$ and $H_2(r)$ in Eqs.~\eqref{dom6} and~\eqref{dom61}
are also invariant under the transformation~\eqref{gauge}.
\par
Like in Section~\ref{SSsec}, we proceed to investigate deformations which do not saturate
the inequalities~\eqref{dom6} and~\eqref{dom61} everywhere by considering positive
functions $H_1(r)$ or $H_2(r)$ which saturate that inequalities only near the boundaries
of the outer region, that is
\begin{equation}
H_1(r)=0
\qquad
{\rm for}
\quad
\left\{
\begin{array}{ll}
r\sim
2\,M
\\
\\
r
\gg
M
\ .
\end{array}
\right.
\end{equation}
In fact, we can still employ the function in Eq.~\eqref{G} and set
\begin{equation}
\label{H}
H_1=M\,G_{\alpha,M}
\ .
\end{equation}
Upon solving~\eqref{dom6} for the corresponding $h$, we obtain
\begin{equation}
\label{dominantg}
h(r)
=
1
-
\frac{1}{r-2\,M}
\left(
\alpha\,\ell
+\alpha\,M\,e^{-r/M}
-\frac{Q^2}{r}
\right)
\ ,
\end{equation}
where $\alpha\,\ell=\ell_0$ and $Q$ is also a constant with dimension of a length and proportional
to $\alpha$.
A second constant of integration was adjusted to meet the proper Schwarzschild limit for
$\alpha\to 0$ (in which we remark that $Q\sim\alpha$ vanishes as well).
The deformation in Eq.~\eqref{dominantg} also has to satisfy the inequality~\eqref{dom61},
which reads
\begin{equation}
\frac{4\,Q^2}{r^2}
\ge
\frac{\alpha}{M}\,(r+2\,M)\,e^{-r/M}
\ .
\end{equation}

Using~\eqref{dominantg} in the line element~\eqref{hairyBH}, we obtain the metric functions
\begin{equation}
\label{dominantBH}
e^{\nu}
=
e^{-\lambda}
=1-\frac{2\,M+\alpha\,\ell}{r}
+\frac{Q^2}{r^2}
-\frac{\alpha\,M\,e^{-r/M}}{r}
\ ,
\end{equation}
which is a sort of ``charged'' version of the solution~\eqref{strongBH} again
with asymptotic mass ${\cal M}=M+\alpha\,\ell/2$.
The effective density is now given by
\begin{equation}
\tilde{\rho}
=
\theta_0^{\ 0}
=
-\tilde{p}_r
=
\frac{Q^2}{k^2\,r^4}
-\frac{\alpha\,e^{-r/M}}{k^2\,r^2}
\label{dendom}
\end{equation}
and an effective tangential pressure reads
\begin{equation}
\tilde{p}_{t}
=
-\theta_2^{\ 2}
=
\frac{Q^2}{k^2\,r^4}
-\frac{\alpha\,e^{-r/M}}{2\,k^2\,M\,r}
\ .
\label{predom}
\end{equation}
We can see that
\begin{equation}
\label{domdom2}
\tilde{\rho}-\tilde{p}_{t}
=
\frac{\alpha\,e^{-r/M}}{2\,k^2\,M\,r^2}(r-2\,M)
\end{equation}
and the DEC is satisfied for $r\geq\,2\,M$, as we originally required.
We can also see that the physical singularity at $r=0$ remains.
\par
The horizon radii $r_{\rm H}$ are given by solutions of
\begin{equation}
\label{horizondom}
\alpha\,\ell
=
r_{\rm H}
-2\,M
+\frac{Q^2}{r_{\rm H}}
-\alpha\,M\,e^{-r_{\rm H}/M}
\ ,
\end{equation}
which allows us to write the metric functions~\eqref{dominantBH} as
\begin{eqnarray}
\label{dominantBHH}
e^{\nu}
=
e^{-\lambda}
&=&
1-\frac{r_{\rm H}}{r}
\left(1+\frac{Q^2}{r_{\rm H}^2}-\frac{\alpha\,M}{r_{\rm H}}\,e^{-r_{\rm H}/M}\right)
\nonumber
\\
&&
+\frac{Q^2}{r^2}-\frac{\alpha\,M}{r}\,e^{-r/M}
\ .
\end{eqnarray}
As with the SEC, it is always possible to choose suitable values
for the parameters $\alpha$, $\ell$ and $Q$ such that analytical solutions for $r_{\rm H}$
can be found.
However, since the DEC requires $r_{\rm H}\geq 2\,M$,
the choice of these values cannot be arbitrary.
We can see this by evaluating the density~\eqref{dendom} at the horizon,
in addition to using the expression~\eqref{horizondom}, which yields
\begin{equation}
\label{condi}
Q^2
\geq
4\,\alpha\,(M/e)^2
\quad
{\rm and}
\quad
\ell
\geq
M/e^2
\ .
\end{equation}
\par
We remark that $Q$ does not need to be an electric charge.
It could be, for instance, a tidal charge of extra-dimensional origin or any other source.
However, when $Q$ represents an electric charge, we can say that the electro-vacuum
of the Reissner-Nordstr\"om geometry also contains a tensor-vacuum whose components
are those explicitly proportional to $\alpha$ in Eqs.~\eqref{dendom} and~\eqref{predom}.
Let us recall that the Reissner-Nordstr\"{o}m metric has two horizons:
the event horizon
\begin{equation}
\label{domhor}
r_{\rm H}
=
M+\sqrt{M^2-Q^2}
<
2\,M
\ ,
\end{equation}
and an internal Cauchy horizon given by
\begin{equation}
\label{cauchy}
r_{\rm CH}
\equiv
M-\sqrt{M^2-Q^2}
<
r_{\rm H}
\ .
\end{equation}
For our solution~\eqref{dominantBH}, we can identify at least three cases for which
the event horizon $r_{\rm H}$ has simple analytical expressions, and the DEC~\eqref{dom1}
and~\eqref{dom2} are satisfied.
As in the Reissner-Nordstr\"{o}m metric, each one of these cases has an internal
Cauchy horizon $r_{\rm CH}<r_{\rm H}$.
\subsubsection*{Case~1}
Let us start by considering the case saturating the inequalities~\eqref{condi},
for which the metric components~\eqref{dominantBHH} become
\begin{equation}
\label{dominantBH2}
e^{\nu}
=
e^{-\lambda}
=
1-\frac{2\,M}{r}\left(1+\frac{\alpha}{2\,e^2}\right)
+\frac{4\,\alpha\,M^2}{e^2\,r^2}
-\frac{\alpha\,M}{r}e^{-r/M}
\ .
\end{equation}
The event horizon is again precisely at $r_{\rm H}=2\,M$, which parallels the case of
Eq.~\eqref{strongh2M}, and we can also write
\begin{equation}
r_{\rm H}
=
\frac{e}{\sqrt{\alpha}}\,Q
\ .
\end{equation}
Notice that by defining
\begin{equation}
{\cal M}=M\left(1+\frac{\alpha}{2\,e^2}\right)
\ ,
\end{equation}
the metric functions~\eqref{dominantBH2} can be written in a more suggestive form as
\begin{equation}
\label{dominantBH2b}
e^{\nu}
=
e^{-\lambda}
=
1-\frac{2\,{\cal M}}{r}
+\frac{Q^2}{r^2}
-\frac{\sqrt{\alpha}\,Q}{2\,r}\,e^{1-2\sqrt{\alpha}\,r/e\,Q}
\ ,
\end{equation}
which can be interpreted as a nonlinear electrodynamics coupled with gravity.
\subsubsection*{Case 2}
\begin{figure}[t]
\center
\includegraphics[width=8cm]{threecases.pdf}
\\
\caption{Metric function for the three different analytic cases with $\alpha=0.8$ and $M=1$
for $\ell=0.4$, $4$, $1$, respectively. }
\label{fig3}
\end{figure}
\begin{figure}[t]
\center
\includegraphics[width=8cm]{general.pdf}
\\
\caption{Effective source terms $\times 10^{4}$ for $\alpha=0.1$, $\ell=0.4$, $Q=0.3$,
with $M=1$.
}
\label{fig4}
\end{figure}
The second case we consider is given by
\begin{equation}
\label{qcase2}
Q^2
=
\alpha\,\ell\,M
\left(2+\alpha\,e^{-{\alpha\,\ell}/{M}}\right)
\ ,
\end{equation}
with $\ell\neq 0$, leading to
\begin{eqnarray}
\label{dominantBH3}
e^{\nu}
=
e^{-\lambda}
&=&
1-\frac{2\,M+\alpha\,\ell}{r}
+\frac{2\,\alpha\,\ell\,M}{r^2}
\nonumber
\\
&&
-\frac{\alpha\,M}{r^2}\,e^{-r/M}\left(r-\alpha\,\ell\,e^{\frac{r-\alpha\,\ell}{M}}\right)
\ .
\end{eqnarray}
The event horizon is now at $r_{\rm H}=\alpha\,\ell=\ell_0\geq 2\,M$.
If we further assume $\alpha\,\ell\sim\,M$, we can express $M=M(Q)$ from~\eqref{qcase2}
and the metric functions~\eqref{dominantBH3} can again be interpreted as a
nonlinear electrodynamics coupled with gravity.
\subsubsection*{Case 3}
Finally, we consider
\begin{equation}
Q^2
=
\alpha\,M\left(2\,M+\alpha\,\ell\right)
e^{-\frac{(2\,M+\alpha\,\ell)}{M}}
\ ,
\end{equation}
so that
\begin{eqnarray}
\label{dominantBH4}
e^{\nu}
=
e^{-\lambda}
&=&
1-\frac{2\,M+\alpha\,\ell}{r}
-\frac{\alpha\,M}{r^2}\,e^{-r/M}
\nonumber
\\
&&
\times\left[r-\left(2\,M+\alpha\,\ell\right)e^{\frac{r-\left(2\,M+\alpha\,\ell\right)}{M}}\right]
\ .
\end{eqnarray}
The event horizon is at $r_{\rm H}=2\,M+\alpha\,\ell=2\,{\cal M}\geq 2\,M$, and the Schwarzschild horizon
is recovered as usual for $\alpha=0$.
As in the two previous cases, the interpretation in terms of nonlinear electrodynamics
is obtained for $\alpha\,\ell\sim M$.
\par
The metric functions for the three analytical cases in Eqs.~\eqref{dominantBH2},
\eqref{dominantBH3} and~\eqref{dominantBH4} are displayed in Fig.~\ref{fig3},
each for a different value of the parameter $\ell$.
In all cases the density and pressures have the same qualitative behavior as
in Fig.~\ref{fig4}, which corresponds to the general case given by
Eqs.~\eqref{dominantBH}-\eqref{predom}.
We conclude that the metric~\eqref{dominantBH} represents a hairy black hole
endowed with the parameters $M$, $Q$, $\alpha$ and $\ell$, where $\{Q,\ell_0=\alpha\,\ell\}$
represents a potential set of charges generating primary hair.
Among this new family of solutions, we can identify three different cases
representing hairy black holes having simple analytical horizons.
All these cases can be interpreted as a nonlinear electrodynamics
coupled with gravity, whose charges are $M$, $\ell_0=\alpha\,\ell$ and $Q$.~\footnote{This way
of presenting the results should not overshadow the fact that $Q^2\sim\alpha$, so that the
Schwarzschild geometry is always recovered for $\alpha\to 0$.}
\par
Finally, we want to end by emphasizing a rather important result.
When the horizon in~\eqref{dominantBHH} has the simple form $r_{\rm H}=K\,M$,
with $K\ge 2$ in order to satisfy the DEC, the metric functions become
\begin{equation}
\label{dominantBHf}
e^{\nu}
=
e^{-\lambda}
=
1-\frac{2\,{\cal M}}{r}
+\frac{Q^2}{r^2}
-\frac{\alpha\,r_{\rm H}}{K\,r}e^{-K\,r/r_{\rm H}}
\ ,
\end{equation}
and the event horizon takes the simple Reissner-Nordstr\"om  form
\begin{equation}
\label{domhorf}
r_{\rm H}
=
\bar{\cal M}
+\sqrt{\bar{\cal M}^2-\bar{Q}^2}
\ ,
\end{equation}
where $\bar{\cal M}={\cal M}/\beta$ and $\bar{Q}^2={Q}^2/\beta$ with
\begin{equation}
\beta=1-\alpha\,\frac{e^{-K}}{K}
\ .
\end{equation}
We conclude that the metric~\eqref{dominantBHf} represents a black hole associated
with some non-linear electrodynamics, whose horizon is related with the Reissner-Nordstr\"om
one by the quite simple expression
\begin{eqnarray}
r_{\rm H}
=
\frac{r_{\rm RN}}{\beta}
\geq
r_{\rm RN}
\ ,
\end{eqnarray}
since $\beta\leq 1$. In order to specify this nonlinear electrodynamics, we identify
\begin{eqnarray}
\label{tmunu}
\theta_{\mu\nu}
=
-\left[
L_{F}\,F_{\mu\alpha}\,F^{\alpha}{} _{\nu}
+L(F)\,g_{\mu\nu}
\right]
\ ,
\end{eqnarray}
where
\begin{equation}
F
=
\frac{1}{4}\,F_{\mu\nu}\,F^{\mu\nu}
\quad
{\rm and}
\quad
L_F=\frac{dL}{dF}
\ .
\end{equation}
In the static spherically symmetric case, we have
\begin{equation}
F_{\mu\nu}
=
E(r)\,\left(\delta^0_\mu\,\delta^1_\nu-\delta^1_\mu\,\delta^0_\nu\right)
\ .
\end{equation}
Following a standard procedure, we then obtain the electric field
\begin{eqnarray}
E(r)
=
\frac{Q}{r^2}
-\frac{\alpha\,  e^{-\frac{K\,r}{r_{\rm H}}} (K\,r+2\,r_{\rm H})}
{4\,r_{\rm H}\,Q}
\ .
\end{eqnarray}
We can describe the underlying nonlinear electrodynamics within the
$P$-dual formalism~\cite{Salazar:1987ap,AyonBeato:1998ub}, which yields
the Lagrangian
\begin{eqnarray}
\label{Lp}
L(P)
=
-4\, \pi\,  P
-\frac{\alpha\,K\,\sqrt[4]{-2\,P}\,e^{\mathcal{G}(P)}}
{4\, \sqrt{\pi }\, \sqrt{Q}\, r_{\rm H}}
\ ,
\end{eqnarray}
with
\begin{eqnarray}
\mathcal{G}(P)
=
-\frac{K\,\sqrt{Q}}{2\, \sqrt{\pi }\, \sqrt[4]{-2\,P}\,r_{\rm H}}
\ ,
\end{eqnarray}
where
\begin{equation}
P
=
\frac{1}{4}\,P_{\mu\nu}\,P^{\mu\nu}
\quad
{\rm and}
\quad
P_{\mu\nu}=L_F\,F_{\mu\nu}
\ .
\end{equation}
\par
We want to conclude emphasizing once again that $Q^2\sim\alpha$,
so that the Schwarzschild geometry is always recovered for $\alpha\to 0$.
However, when $Q$ represents an electric charge, we can say that the
electro-vacuum (Reissner-Nordstr\"om geometry) is filled with a tensor-vacuum
whose origin lies in the nonlinear electrodynamics with the Lagrangian~\eqref{Lp}.
\section{Conclusions}
\label{Scon}
Using the EGD approach, we studied the emergence of hairy black holes due to matter
surrounding the central source of the Schwarzschild metric.
Demanding that the solution always admits a well defined horizon through Eq.~\eqref{constr1},
and that the hair satisfies the SEC or DEC through Eqs.~\eqref{strong01} or~\eqref{dom1}
and~\eqref{dom2}, respectively, we found two new families of hairy black holes displayed
in Eqs.~\eqref{strongBH} and~\eqref{dominantBH}.
These geometries were analysed and, in particular, we found that the solutions
satisfying the DEC contain the non-trivial extension of the Reissner-Nordstr\"om
black hole shown in~\eqref{dominantBHf} which possesses a simple event horizon.
The Lagrangian of the nonlinear electrodynamics, which sources this solution, was also
obtained explicitly.
\par
From the technical point of view, since aim of the present work was to study some general
conditions under which hair can be added to the (spherically symmetric) vacuum
black holes of general relativity, the EGD was the natural approach to employ from the onset.
In fact, the EGD is precisely devised for describing deformations of known solutions
of general relativity induced by adding extra sources.
Moreover, the properties of the added source were restricted in order to enforce
the conditions mentioned above, rather than assuming the hair is described in terms
of fundamental fields.
Nonetheless, we were able to give a description in terms of a nonlinear electrodynamics
at least in one specific case.
\par
Finally, we would like to remark that the charges $Q$ and $\ell_0=\alpha\,\ell$
associated with our hairy black holes admit simple physical interpretations.
The charge $Q$ can be viewed as an effective electric charge and is proportional
to $\alpha$, which is the generic parameter measuring the deviation from the chosen
vacuum solution (which is given by the Schwarzschild metric).
A special mention deserves the parameter $\ell_0$, which is associated with gauge
transformations of the seed Schwarzschild metric and which seems to always push
the event horizon to radii larger than the Schwarzschild radius.
Therefore $\ell_0=\alpha\,\ell$ measures how much the entropy of the black hole increases from
its minimum Schwarzschild value $S=4\,\pi\,{M^2}$ when hair is added.
\subsection*{Acknowledgments}
R.C.~is partially supported by the INFN grant FLAG and his work has also been carried out in the framework
of activities of the National Group of Mathematical Physics (GNFM, INdAM) and COST action {\em Cantata\/}.

redpajama_set_name: RedPajamaArXiv


text:
Diversity, Equity, and Inclusion Statement
Diversity, Anti-Racism, Equity and Inclusion Training
PET SURVEY
Funding Application for 2023
Our Funded Agencies
Charity Tracker
Workshops & Free Webinars
Register Your Agency
Allocations Team Volunteer
Volunteer Response Center (VRC)
GIVE Awards
PVSA Awards
Campaign Videos
2023 eCampaign Handbook
2022 Funded Agencies
Company Pledge Form
Top 10 Reasons to Give
Campaign T-Shirts
2023 Campaign Donation
What is a VISTA
VISTA Application
VISTA Reports
Thriving as a Culture of Diversity
POLICY ON DIVERSITY & INCLUSION
The United Way of Lowndes and Noxubee is committed to be a model of diversity and inclusion, and to promote an inclusive culture where diversity is valued by everyone. This includes our Board of Directors, staff, volunteers and allocation agencies, reflecting the many faces, cultures and walks of life that make up the communities we serve. It is central to our mission to bring together caring people to more effectively address the issues that face our communities.
Our strength comes from our diversity and we celebrate the visible and invisible qualities that make each person unique, including race, gender, age, sexuality, ability, religion, national origin, gender identity, and other identities. We respect, value, and celebrate the unique attributes of our stakeholders and we believe that no one should be discriminated against because of these qualities.
We commit to aligning our culture and business practices to be a beacon of diversity, equity, inclusion, and belonging for all people. We will practice this commitment by:
Creating a Diverse and Inclusive Workplace. United Way of Lowndes and Noxubee is committed to building and maintaining an environment that embraces and values differences. Employees should feel valued and respected, without bias or preference based on difference. Everyone should be treated with dignity and respect.
Modeling leadership and developing practices and policies that embrace the value of "inclusion" in our day-to-day operations that promote understanding and acceptance of individual differences.
Supporting programs and initiatives that advance the recognition, understanding and importance of safeguarding the right to dignity and justice of all people.
Continuing to seek respectful relationships and partnerships that are aligned with achieving common goals, both within and outside of United Way of Lowndes and Noxubee, that are inclusive of individual ideals, abilities, and opinions.
Respect and Inclusion of Diverse Volunteers. To be relevant and a viable community partner, staff and volunteers model an awareness of, and understanding and respect for, the many forms of difference reflected in the people and communities served by United way of Lowndes and Noxubee.
United way of Lowndes and Noxubee will comply with all statutes, regulations, and executive orders that address equal employment and non-discrimination to select the individual considered best qualified on the basis of ability and merit and without regard to race, religion, creed, color, national origin, ancestry, citizenship, sex, military status, age, marital status, sexual orientation, gender expression or identity, genetic information, disability, or any other personal characteristic protected under applicable federal, state or local law. There will be no discrimination on any of these grounds in employment, recruitment, hiring, compensation, training, advancement opportunities, or any other aspect of employment.

redpajama_set_name: RedPajamaCommonCrawl


text:
Establishment of a Gene Expression System in Ochrobactrum anthropi
Mohamed N. Seleem, Mohammed Ali, Stephen M. Boyle, Biswarup Mukhopadhyay, Sharon G. Witonsky, Gerhardt G. Schurig, Nammalwar Sriranganathan
Mohamed N. Seleem
Department of Biomedical Sciences and Pathobiology, Center for Molecular Medicine and Infectious Diseases, Virginia-Maryland Regional College of Veterinary Medicine
Department of Forensic Medicine and Toxicology, Faculty of Veterinary Medicine, Assiut University, Assiut, Egypt
Stephen M. Boyle
Biswarup Mukhopadhyay
Virginia Bioinformatics Institute, Virginia Polytechnic and State University, Blacksburg, Virginia
Sharon G. Witonsky
Gerhardt G. Schurig
Nammalwar Sriranganathan
For correspondence: nathans@vt.edu
Genetic studies of Ochrobactrum anthropi are hindered by the lack of a suitable gene expression system. We constructed a set of vectors containing several promoters and a His tag fusion in the N terminus to facilitate protein detection and purification. The new vectors should significantly enhance the genetic manipulation and characterization of O. anthropi.
Ochrobactrum strains are of particular interest for bioremediation (6). They are capable of degrading organophosphorus pesticides such as parathion and methylparathion (17), phenol (2), the toxic organic solvent dimethylformamide (14), petroleum waste (4), and the soil contaminant chlorothalonil (5). They are also capable of removing chromium, cadmium, copper, and toxic metals from the environment (10). Unfortunately, genetic studies with Ochrobactrum isolates have been hindered by the lack of an efficient system for gene expression and purification of recombinant proteins.
Our goal in this research was to establish an enhanced gene expression system in Ochrobactrum anthropi to enhance genetic manipulation and characterization and to allow rapid and easy one-step purification of recombinant proteins directly from O. anthropi.
The oligonucleotides used in this study are listed in Table 1. Recombinant DNA methods were used according to standard techniques (11). PCRs were performed using Platinum PCR SuperMix High Fidelity (Invitrogen). Restriction and modification enzymes were purchased from Promega. A QIAprep spin miniprep kit from QIAGEN was used for all plasmid extractions, and a QIAGEN PCR cleanup kit was used for removal of all restriction enzymes and for DNA gel extraction.
Primers used to amplify the promoters
The sequence carrying the origin of replication (rep), the chloramphenicol acetyltransferase gene (cat), and the multiple cloning site (MCS) of the broad-host-range pNSGroE Brucella expression vector (GenBank accession number AY576605) (13) was used as the backbone for the construction of the new vectors. The Brucella abortus groE promoter was excised from pNSGroE with the SalI and BamHI restriction enzymes, and the promoterless pNS construct was used for promoter replacement.
The chloramphenicol resistance gene promoter (Ch) was amplified from the broad-host-range pBBGroE expression vector (15) with primers Ch-F and Ch-R. In the reverse primer, six histidine residues and one glycine residue were engineered after the translational start codon to facilitate epitope tagging at the amino terminus by fusing a minimum number of amino acids to any expressed protein (13). To avoid the translational error or inhibition arising from rare codon bias (7), the preferred codon usage of Ochrobactrum spp. (http://www.kazusa.or.jp/codon/cgi-bin/showcodon.cgi?species=Ochrobactrum+anthropi+%5Bgbbct%5D) for histidine and glycine was used. After restriction digestion and purification, the Ch promoter was cloned into the pNS construct to form the pNSCh expression vector (Fig. 1).
Plasmid map. Shown are the engineered pNSCh and pNST5 expression vectors for constitutive and regulated expression, respectively, with the His tag fusion in the N terminus. cat, chloramphenicol acetyltransferase gene conferring chloramphenicol resistance; rep, gene required for plasmid replication; 6×His, His tag fusion; LacO, lac operator for regulated expression.
The kanamycin resistance gene promoter (Kan) and the ampicillin resistance gene promoter (Amp), each containing a His tag fusion in the N terminus, were amplified and cloned in the same way as was Ch by using the pUC4K cloning vector (Pharmacia)and primers Kan-F and Kan-R for Kan and the pRSETA expression vector (Invitrogen) and primers Amp-F and Amp-R for Amp.
The coliphage T5 promoter (16) with the downstream lac repressor, a synthetic ribosomal binding site (RBSII), and the His6 tag codon sequence was excised with XhoI and BamHI from the pQE-40 expression vector (QIAGEN) and ligated to the pNS construct to form the pNST5 expression vector (Fig. 1).
The hybrid TrcD promoter (1) with the downstream bacteriophage gene 10 translational enhancer (9) minicistron, reinitiation ribosome binding site (12), and lac repressor was amplified from the pTrc2HisA vector (Invitrogen) and ligated to the pNS construct to form the pNSTrcD expression vector.
In order to study the expression and activity of the cloned promoters inside O. anthropi, the promoterless Escherichia coli β-galactosidase gene (lacZ) was amplified from pRSETB/β-gal (Invitrogen) as described previously (13) and cloned into all expression vectors downstream of the various promoters. A colorimetric assay (15) was employed to compare the levels of β-galactosidase expression.
A promoterless green fluorescent protein (GFP) gene (gfp) was excised from the pGFPuv vector (BD Biosciences Clontech), cloned into the MCS of pNSTrcD, and used for Western blotting and protein purification.
The lacZ constructs and the pNSTrcD-gfp expression vector with gfp expressed under the control of the TrcD promoter were transformed into O. anthropi strain 49237 as described previously (8). The gfp was purified from recombinant O. anthropi using nickel-nitrilotriacetic acid (Ni-NTA) agarose (QIAGEN) and 6 M guanidine HCl. Imidazole and β-mercaptoethanol (both at 20 mM) were added to the lysis buffer, and 1% Triton X-100 and 250 mM NaCl were added to the washing buffer to reduce contaminating proteins. The cells were pretreated with TE-citrate-Zwittergent 3-14 (10 mM Tris, 1 mM EDTA, pH adjusted to 4 with citric acid, 1% Zwittergent 3-14) for 2 h at 55°C prior to purification. The concentration of the purified recombinant protein was determined by the bicinchoninic acid protein assay kit (Pierce) using the manufacturer's enhanced test tube procedure after removal of urea by Microcon YM-10 centrifugal filter devices (Millipore). The purity of the extracted protein was determined by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE).
To test the fusion of the His epitope tag and the efficiency of detection, Western blot analysis was performed by separating the total-cell lysates of recombinant O. anthropi expressing gfp under the control of the TrcD promoter by 10% SDS-PAGE, followed by transfer to one of two nitrocellulose membranes (Osmonics). One membrane was incubated overnight with a mixture of a horseradish peroxidase (HRP)-conjugated anti-HisG antibody (1:3,000) (Invitrogen) and peroxidase-conjugated anti-His6 (Roche) (1:3,000). The second membrane was incubated overnight with an anti-His6 antibody (Roche) (1:1,000) and then for 1 h with HRP-conjugated anti-mouse secondary antibodies (1:1,000) (Kirkegaard & Perry Laboratories).
The sizes and descriptions of the vectors are given in Table 2.
Descriptions of plasmids constructed and used in this study
Figure 1 diagrams the pNSCh expression vector, which was introduced into O. anthropi with an efficiency of 2.1 × 109 transformants per μg DNA. Due to the reduction in size, the new plasmids (∼3 kb) were 1.6 × 103 times more efficient at transformation than the broad-host-range expression vector pBBGroE (5.9 kb) (15). All plasmids were stably maintained after 8 serial passages over 16 days on tryptic soy agar plates in the absence of chloramphenicol selection.
All amplified promoters were able to express β-galactosidase inside O. anthropi with various strengths (Fig. 2). The B. abortus constitutive groE promoter was the strongest promoter. The results indicate that the vectors constructed may be used in O. anthropi as reporters of gene expression and promoter activity. The anti-His antibodies were used successfully to detect the expression of GFP fused with the His tag (Fig. 3). The N-terminal His tag fusion allowed one-step purification of 7.3 mg of recombinant GFP from 100 ml of bacterial culture (optical density at 600 nm, 2). Figure 4 shows the purity of the purified recombinant protein.
LacZ activity from different promoters in O. anthropi. The LacZ activity of each construct was determined as described in the text for expression of β-galactosidase and is represented in Miller units. Each bar represents the average of three separate cultures. Triplicate cultures were used in each experiment.
Western blot of recombinant GFP. Shown is the detection of the His-tagged GFP fusion protein expressed from the TrcD promoter in O. anthropi. (A) The membrane was incubated with an anti-His6 antibody (1:1,000) overnight and with HRP-conjugated anti-mouse secondary antibodies (1:1,000) for 1 h. (B) The membrane was incubated with a mixture of an HRP-conjugated anti-HisG antibody (1:3,000) and peroxidase-conjugated anti-His6 (1:3,000) overnight. M, Precision Plus Protein dual-color standards (Bio-Rad).
SDS-PAGE of purified recombinant GFP. The cells were pretreated with TE-citrate-Zwittergent 3-14 for 2 h at 55°C prior to purification of GFP from O. anthropi using Ni-NTA agarose (QIAGEN). The SDS-PAGE gel was stained with Coomassie blue. Lane 1, total-cell lysate of recombinant O. anthropi; lanes 2 to 4, purified recombinant GFP elutions 1 to 3; MW, Precision Plus Protein dual-color standards (Bio-Rad).
In this study we report the construction of a series of expression vectors for O. anthropi that can be used for heterologous gene expression and for protein detection and purification.
The lacZ and gfp genes were introduced into O. anthropi and expressed under the control of various promoters. Recombinant GFP was detected by Western blotting using anti-His antibodies and purified using Ni-NTA. The newly described vectors will enhance genetic manipulation and characterization and will facilitate the use of O. anthropi as a potential bioremediation tool and a biopesticide agent.
Nucleotide sequence accession numbers.
The sequences of all the vectors reported in this paper have been deposited in GenBank under the accession numbers listed in Table 2.
Received 22 June 2006.
Amann, E., J. Brosius, and M. Ptashne. 1983. Vectors bearing a hybrid trp-lac promoter useful for regulated expression of cloned genes in Escherichia coli. Gene 25:167-178.
El-Sayed, W. S., M. K. Ibrahim, M. Abu-Shady, F. El-Beih, N. Ohmura, H. Saiki, and A. Ando. 2003. Isolation and identification of a novel strain of the genus Ochrobactrum with phenol-degrading activity. J. Biosci. Bioeng. 96:310-312.
Fengqing, H., and Y. Song. 2005. Electroporation-mediated transformation of Aeromonas hydrophila. Plasmid 54:283-287.
Katsivela, E., E. R. Moore, D. Maroukli, C. Strompl, D. Pieper, and N. Kalogerakis. 2005. Bacterial community dynamics during in-situ bioremediation of petroleum waste sludge in landfarming sites. Biodegradation 16:169-180.
Kim, Y. M., K. Park, G. J. Joo, E. M. Jeong, J. E. Kim, and I. K. Rhee. 2004. Glutathione-dependent biotransformation of the fungicide chlorothalonil. J. Agric. Food Chem. 52:4192-4196.
Lebuhn, M., S. Bathe, W. Achouak, A. Hartmann, T. Heulin, and M. Schloter. 2006. Comparative sequence analysis of the internal transcribed spacer 1 of Ochrobactrum species. Syst. Appl. Microbiol. 29:265-275.
Makrides, S. C. 1996. Strategies for achieving high-level expression of genes in Escherichia coli. Microbiol. Rev. 60:512-538.
McQuiston, J. R., G. G. Schurig, N. Sriranganathan, and S. M. Boyle. 1995. Transformation of Brucella species with suicide and broad host-range plasmids. Methods Mol. Biol. 47:143-148.
Olins, P. O., C. S. Devine, S. H. Rangwala, and K. S. Kavka. 1988. The T7 phage gene 10 leader RNA, a ribosome-binding site that dramatically enhances the expression of foreign genes in Escherichia coli. Gene 73:227-235.
Ozdemir, G., T. Ozturk, N. Ceyhan, R. Isler, and T. Cosar. 2003. Heavy metal biosorption by biomass of Ochrobactrum anthropi producing exopolysaccharide in activated sludge. Bioresour. Technol. 90:71-74.
Sambrook, J., E. F. Fritsch, and T. Maniatis. 1989. Molecular cloning: a laboratory manual, 2nd ed. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, N.Y.
Schoner, B. E., R. M. Belagaje, and R. G. Schoner. 1987. Expression of eukaryotic genes in Escherichia coli with a synthetic two-cistron system. Methods Enzymol. 153:401-416.
Seleem, M. N., R. Vemulapalli, S. M. Boyle, G. G. Schurig, and N. Sriranganathan. 2004. Improved expression vector for Brucella species. BioTechniques 37:740, 742, 744.
Veeranagouda, Y., P. V. Emmanuel Paul, P. Gorla, D. Siddavattam, and T. B. Karegoudar. 2005. Complete mineralisation of dimethylformamide by Ochrobactrum sp. DGVK1 isolated from the soil samples collected from the coalmine leftovers. Appl. Microbiol. Biotechnol. 71:369-375.
Vemulapalli, R., Y. He, S. M. Boyle, N. Sriranganathan, and G. G. Schurig. 2000. Brucella abortus strain RB51 as a vector for heterologous protein expression and induction of specific Th1 type immune responses. Infect. Immun. 68:3290-3296.
Wang, Y., A. Mukhopadhyay, V. R. Howitz, A. N. Binns, and D. G. Lynn. 2000. Construction of an efficient expression system for Agrobacterium tumefaciens based on the coliphage T5 promoter. Gene 242:105-114.
Zhang, R., Z. Cui, J. Jiang, J. He, X. Gu, and S. Li. 2005. Diversity of organophosphorus pesticide-degrading bacteria in a polluted soil and conservation of their organophosphorus hydrolase genes. Can. J. Microbiol. 51:337-343.
Applied and Environmental Microbiology Oct 2006, 72 (10) 6833-6836; DOI: 10.1128/AEM.01446-06
You are going to email the following Establishment of a Gene Expression System in Ochrobactrum anthropi


text:
You are here: Home / Entertainment / Celebs / #RememberingPrince: Friends, Acquaintances & Fans Share Their Stories of the Purple One
#RememberingPrince: Friends, Acquaintances & Fans Share Their Stories of the Purple One
By Trey Speegle on April 22, 2016 5:10 pm
It's sad when people leave suddenly, especially when we admire but don't really know them. But one way people remain "alive" is through remembering them. I love hearing random encounters and thoughts about Prince, and I thought I'd share a few friends' stories here, including my own minor one…
"My story is not about a direct encounter with Prince, I never met him, rather it's a funny story that was told to me by someone in our stage crew on tour in 1989-90, who left for a while to work with Prince, then returned to work with us again. He said that whenever Prince saw him, he would ask,
'Who's that little band you were with… they sing that little song, then he would sing in his falsetto voice, love shack, baby Love Shack?'" –The B-52s', Keith Strickland
"Chi Chi (Valenti) and I are battling over the best description of Prince. My favorite was by L.A. Reid, 'He could steal your woman wearing high heels.'
Chi Chi's was by Robert Christgau on seeing Prince for the first time: 'Mick Jagger should fold up his penis and go home.'" –DJ, Johnny Dynell
"The first time I laid eyes on him was at the Ritz in December 1980 where I was djing and he was playing for the Dirty Mind tour. The Ritz was still a fairly new venue opening in May of that year. That was the show that changed it all. For me, for the Ritz and I think for Prince too. It was insane. He came back again and played in March of 1981. Lucky to have witnessed that and all that came after. Saw him many times after and obviously was a massive influence. All the bands and artists he worked with, the careers he is responsible for is pretty astounding. I really used to love when he put out those non lp b-sides "She's Always in My Hair", "Erotic City", "17 Days". Just too good. He will be so missed, but damm he seemed to do it all and did it on his own terms. Pop life. The artist." –Justin Strauss
"Prince in Rio! I had the pleasure of being backstage at Rio's Maracanã Stadium during 1991's edition of Rock In Rio festival. There was a massive sense of anticipation for his arrival and security was super tight. I had a quick peek into his dressing room – It was all customized in purple drapes, purple pillows, purple candles, purple everything… Then suddenly more excitement as he entered the stadium and passed in front of me with his private security team lead by this beautiful woman! There was a lock down in the corridors, no one could really move around. Then I went down to see his concert from the grass and will never forget the looooooong and out of this world rendition of Purple Rain he played on his Purple piano!!!! Prince was an amazing music innovator and a true pop star in the old school sense of the term! He blew the stadium away!! Shine on Purple Star!" –producer, Béco Dranoff
Prince by Warhol, 1984
"My story isn't a direct encounter with Prince either but I remember this vividly. I was working for Vanity Fair in the art department and we were doing a story on the Prince phenomenon, and hired Andy Warhol to do the illustration for the story. (I still have a hard proof of the one shown here.) For some reason, I got invited to a screening of Purple Rain which was in a theater in Times Square. It was not the kind of red carpet premiere you have today, and Prince wasn't there, but this new singer who was starting to get hot at the time was; Madonna. She was with her friend Debi Mazar, who I knew at the time and they sat directly in the row in front of us and said hi coming in. I remember Madonna REALLY rocking out and SUPER into the music all through the film as we all were. Prince & Madonna were just about THE hottest things on the planet in '84, and there they were (sort of) right in front of me. It was a moment." –artist/blogger, Trey Speegle
"Michael Jackson, Prince, Madonna, products of very religious upbringings: a Jehovah's Witness, a Seventh Day Adventist turned Jehovah's Witness, and a deep Catholic school girl named for the Virgin Mother and at war with 'the father.' Very interesting to consider together. All–at the same, high 80s moment, really– acting out the freedom of the body and explosive sexuality, exorcising demons, trying to get free, producing music where sexual and religious images mingled, creating more powerful new selves. So much rebellion, conflict, creativity. Yet classic American strivers. Messy inside but unparalleled, perfectionistic professionals, worker bees, hitting the mark at any cost. But the men both seemed so personally conflicted and tortured inside. Michael for sure. Don't need to repeat that story. Prince, still sometimes needing to project 'ladies man' though as seemingly gender-complex as M.J., perhaps struggling more privately as it seems that he was actually conservative and somewhat uncomfortable with gays, himself. Intensely private and mysterious yet exhibitionistic. How did their race figure? Even their size–diminuitive and fey and kind of the antithesis of the desirable male in black culture, but creating their own kind of power, perhaps out of necessity…
All suffering intense physical pain for the work and one dead from a pain-killer. Excruciating/exquisite control of the body and maniacal control of the work, but not the head or heart. No big thesis, just scattered thoughts. So much going on inside those beautiful ones, intensity and creativity on fire. Driven. I miss the moment when they reigned, those sexy hymns we danced to. Exciting. Maybe just because I was young. Maybe because I am still struggling." –Author, George Hodgman
"When I was 18 years old and studying in Paris at the time I was a resident dj in this club called Montana. One night the manager of the club called me and said that Prince had requested to have the club privatized for him and a few friends and that he specifically asked that I play the music after hearing me a few nights before. Keep in mind that I was a huge fan of Prince since a very young age and that I would play his records on vinyl as a little toddler in my Dads studio.
"The song 'Kiss' is in my top 10 favorite songs of all time. I was very excited when I got the call as you can imagine. To make a long story short… Prince showed up around 3ish after I had been playing an empty dance floor for about 4 hours already. He walked in with this gorgeous woman that, I kid you not was twice his size (even with the 5 inch heels he had on) . I was playing a lot of funk and disco which he seemed to be enjoying and dancing to. Fifteen minutes into the party he requested that I play a few of his songs. I played "let's dance" by Bowie followed by "Kiss". He turned around and gave me a thumbs up. Seconds after hearing his record drop, he leaned in to his date of the night and kissed her on the lips at the exact moment he says kiss in the song.
I continued playing his music until he came back in the DJ booth and asked for some James Brown. He danced a little bit longer and took his friends and date back to his Paris home. He did not sit down the whole night while I was spinning. Before he left he thanked me, shook my hand with his leather gloves he was wearing and told me I was a talented disc jockey. It was a surreal moment for me at the time and I can easily say it is one of the highlights of my 'DJ career'. I recorded the mix from that night which I will be uploading in the next few weeks after some digging through my laptops. Deeply saddened by this news today. I am currently in london where I will be spinning his music tonight in his honor. #RIP to the master of psychedelic rock and intergalactic funk. A true musical genius, icon and most of all a genuine nice person. My condolences to all his close ones." –DJ, Lino Meoli, son of Maripol
"The audacity of Prince Rogers Nelson did not flower with fame and purchase –did not even begin with music, since by all accounts he strode with slight stature onto a junior high school basketball court, throwing shade with the same shy-but-Sly buoyancy we would all witness later in performance. He laid down the law like a landing strip in the rain forest, his flickering lights serving as our clearance from the tower, all touching down safely behind him. He was possessed of the ecstasy of Little Richard, the locomotion of James Brown; the fusing spark-shower of Jimi Hendrix. He understood the sublime and abstracted alchemy of Miles [Davis], the impatient genius of Ray [Charles]; the giddy volatility of Sly Stone, the cat-and-mouse come-on of Marvin Gaye. He embodied the Saturday night/Sunday morning disparities of the Reverend Al –and his persona was as cunning and confounding as that of Salvador Dali.
I have ceased distinguishing between the religious and the secular, for everything is holy: our courage and humility, our senses both lost and found; our love and our lust…all that shall swoon and couple, leaving in their wake the real hope that, late as is the hour –with as much as we have been given and squandered; as little as we might deserve it, though we stomp and plead— there may yet be more on offer: God willing, just one more song sung into high rafters before we are finally called to quit and disperse." –musician and producer, Joe Henry (posted by photographer Maude Schuyler Clay)
Kevin Sessums is to the right of Prince,
critic Gene Siskel on the left…
"I had greeted him as he came into the party and had just admired his ass in that jumpsuit which Siskel kidded me for so obviously doing. Then later I went up to his bodyguard standing right next to him and knowingly played the game.
'May I speak to Prince?'
I asked the bodyguard as Prince listened above the din and dared to smile at my knowingness. This was Vanity Fair's first Oscar party at Morton's in 1994 and he was the biggest star in the room. Yet no one else seemed to be going up to him. The bodyguard looked down at The Diminutive One who, in turn, nodded his approval – knowingly.
'Yeah, you can,'
the bodyguard said. So, Prince and I had a little Oscar party tete-a-tete.
'Gigolos get lonely too, huh,'
I said to get his attention – which it did. I then told him about the one time I ever saw him perform. It was the Purple Rain tour in Daly City at the Cow Palace. I was visiting San Francisco for the first time and a friend, Adam Block, who was the music critic for the Advocate, had prime seats right next to the stage. I also told him his jump suit made his ass look hot. He lowered those eyelids of his, deciding if he should take that as a compliment or a threat. I wasn't sure if he was going to hit me with his walking cane. He tapped me on my own butt instead.
'You're right.' he said.
And laughed – knowingly – a gigolo giggle, amusement gargled back down in his throat where those guttural notes could be grunted out amidst those airy high ones that could so shockingly take flight as he himself now has." –Author, Kevin Sessums
"I was working the door at the ex-Sound Factory (after Ingrid Casares gave up trying to turn it into something else and before it became Twilo). Saturday nights were big, and on this particular one during fashion week Donatella Versace was having a private party for her 1998 ad campaign with Courtney Love. Mobbed confusion at the door all night, lots of famous faces. At some point a beefy guy in a suit approached the side and said,
'I've got Prince in the car over there for the Donatella party but he doesn't like being bumped or hassled by people."
He motioned to a limo across the street. I told him to get my attention when ready, and I'd make sure there was a path they could sneak through quickly on the side. He got back in the limo and drove off. A half hour later the same limo slowly pulls up right in front of the crowd, not the side, and the guy gets out and looks at me. I motioned him to the side but it was too late.
Slowly out of the door of the limo emerges, not Prince, but five tall, beefy security guards in matching dark suits, with arms locked in a circle to form a sort of human cage, their open Prada jackets making a curtain. I yelled for people to back-up as this contorted, human tarantula sloooowly crawled out of the limo (two of the bodyguards facing backwards) and inched towards us. It was an acrobatic wonder! People stared. The crowd naturally parted for such a spectacle.
New Yorkers (back then) didn't yell or take pictures around famous people, they'd just go weirdly quiet. But who were we gawking at? They didn't know. I wasn't sure. It could've been anybody! Sure enough, as I lifted the velvet rope and they wobbled their way into the door I caught a square-inch of purple from inside the walking flesh cage.
An hour later, Rob Fernandez came out and said,
'Prince wants to leave.'
And as the same human contraption inched it's way out of the club (this time in reverse), I heard a muffled but unmistakable voice from deep inside say,
'Thank you.'
It crawled back in the limo and drove off. A security guard turned and asked me,
'Was that really Prince?'
I said, 'It had to be.'
–Sock Job director, Mark Allen
Filed Under: Celebs, Entertainment, Featured, Music


It looks like this bout might actually happen! We might actually get Conor McGregor vs. Floyd Mayweather in a boxing ring. If you put this kind of thing in a movie people would react by saying "Oh come on, in real life there is no way such a bout would be arranged." In real life however, Conor McGregor is far more interesting than anything fiction could come up with.
As for whether or not Conor has a shot however, that is another story. Many experts are stating that Conor has no chance at beating Floyd. Others, usually MMA fans, state their belief that Conor has a "puncher's chance" in the bout. Joe Rogan recently stated that Conor has a "death touch" that Floyd should be wary of.
The other factor is that there is no telling how Conor plans on approaching this fight. What if he went in and just charged straight at Mayweather with his hands down? Floyd's used to fighting boxers, not a crazed madman like Conor McGregor. Plus Mayweather can't knock Conor out, he doesn't hit hard enough to do that. So basically Floyd will have to avoid getting hit by Conor throughout the fight and occasionally score enough points to win a decision. . Luckily for him, he's made a career of making top notch strikers miss.
Some may believe it unlikely that Conor wins, but considering nobody has ever seen something like this bout before, how can anyone be sure?
Here are 15 things you didn't know about Conor McGregor and Floyd Mayweather.
Not surprisingly, both Floyd Mayweather and Conor McGregor have been fighting since a very early age. Floyd Mayweather Sr. has told reporters that he was teaching Floyd Jr. how to throw punches as early as the age of one. Floyd Mayweather Sr. was a boxer as well. The senior Mayweather sported an impressive 28-6-1 record in his career which spanned from 1974 to 1990.
As for Conor, his father, Tony McGregor, enrolled him in boxing at the age of 12. While that is a solid 11-year difference between McGregor and Mayweather, it is still a fairly young age. According to Tony, the young Conor McGregor was so excited after his first boxing lesson that he started questioning his parents as to why they enrolled him in football for so many years.
Floyd Mayweather Jr.'s professional boxing record is 49-0, but he's also undefeated at WrestleMania. In 2008, Floyd "Money" Mayweather was paid over $20 million to take on the Big Show at WrestleMania 24.
Boxers such as Mike Tyson and Muhammad Ali had made appearances in pro-wrestling before, but not like this. Mayweather wrestled a full match with Big Show, one that was arguably the most entertaining on the show.
Conor, on, the other hand, has also had his run-ins with the WWE roster. Leading up to his UFC 202 rematch with Nate Diaz, Conor made disparaging remarks about the WWE roster which went viral. Since that time, Triple H has publicly commented on wanting Conor to make an appearance at a WrestleMania similar to Floyd's from 2008.
Before Conor McGregor was an MMA superstar, he was a plumber. Eventually Conor would decide to quit that career path in order to focus on fighting full-time. At the time Conor was living at home and training MMA part-time without his parents knowing. His father Tony once commented that he knew his son wasn't going to be a plumber instantly one morning when he went to wake the future star in time for his shift, and Conor refused to budge. He told his father that being a plumber just wasn't for him, and would be fighting in Cage Warriors shortly after.
As for Floyd, there was never any other career path considered. He made his pro debut at 19 years old, but he had been making an impact in boxing before then even.
Floyd Mayweather has not competed outside of Nevada since 2005. His last 14 bouts have all been in Las Vegas, with 12 of them being held at the MGM Grand. A similar, but less pronounced trend has started to occur in Conor McGregor's schedule as well. Five of Conor's last seven bouts have all been held in Las Vegas.
Mayweather was more prone to travel earlier in his career, but has never had a professional boxing bout outside of the United States. Conor too started his career primarily fighting in his home country of Ireland. His first 10 fights were in Ireland, and he wouldn't make his American debut until signing with the UFC. His second UFC bout was in Boston, a city which consists mainly of people with Irish roots. Not much of a stretch.
Conor McGregor is not the only athlete in the family. His sister Erin, who at 34 years of age is six years Conor's senior, was a professional bodybuilder.
Erin McGregor is regularly seen inside the octagon following a victory by her younger brother, but when she is not there in person she is always cheering him on. She credits Conor with helping to motivate her to go into professional bodybuilding. Likewise, Conor has credited his sister with helping to motivate him in his career.
Erin is said to have won multiple competitive events in her time, but has not competed recently after deciding to start a family.
Floyd meanwhile also has three sisters, and one brother. His brother, Justin Mayweather is also a pro boxer. Justin has a 3-0 record, having last fought in February of 2016.
In 2014, rapper and former Mayweather buddy 50 Cent put down a challenge for Floyd: If Floyd could read aloud one page from a Harry Potter book, 50 Cent would donate $750,000 to charity.
Mayweather did not respond by reading the Harry Potter book, instead he posted several photos of cheques he'd earned from big fights. Posting pictures of cheques, however, is not the same skill-set as reading. It is unclear if this was pointed out to Floyd or not. While Floyd claims he is literate, there seems to be little evidence of this.
While no one is claiming Conor to also be illiterate, he did post a photo of himself relaxing on a plane reading an upside-down newspaper on Instagram once. That sort of got people wondering a little.
Conor McGregor and Floyd Mayweather are both businessmen more than anything else. As such, they are always looking down the avenues which will make them the most money. Mayweather is 40 years old and already retired twice, and boxing is something he won't be able to continue into old age. As for Conor, he knows that his superstardom will translate to other forms of entertainment, ones much easier than a third fight with Nate Diaz would be.
Floyd Mayweather most recently made a cameo appearance in Think Like a Man Too, and also had a run on Dancing with the Stars.
Conor McGregor, meanwhile, has landed a small role in the upcoming season of Game of Thrones, and has voiced a character for the Call of Duty video game. Many more roles are sure to come.
Mike Tyson does not like Floyd Mayweather. The two former friends had a falling out for reasons no one is discussing. Tyson also has taken issue to Mayweather stating he is the greatest boxer of all time. Tyson considers this an insult to Muhammad Ali.
Mike Tyson stated long before the bout between Floyd and Conor became realistic, that he would happily train Conor on how to knock Floyd out. In fact, Tyson has visited Floyd during training camps before and in May of 2015 the two were spotted sitting together cage side at a UFC event.
Tyson had been scheduled to coach Chris Brown in a charity bout against Soulja Boy who would be coached by Floyd Mayweather this year, but the bout was ultimately cancelled.
Conor McGregor's second fight in the UFC was one of his most challenging to date. Not only was he up against the current interim featherweight champion Max Holloway, but he tore his ACL in the second round.
The fight was Conor's first ever in the United States, and second in the UFC. Despite the injury, Conor would go on to earn a unanimous decision victory over his popular Hawaiian opponent.
McGregor blames the injury for his not being able to finish Holloway in the fight, and also claims the injury impacted his performance in his next fight against Chad Mendes. He has claimed he beat Mendes "on one leg."
Mayweather, on the other hand, is said to suffer from what his trainers call "fragile hands" that some claim have prevented him from knocking out opponents throughout the years.
Both Conor McGregor and Floyd Mayweather know what it is like to experience poverty, though for different reasons. Mayweather grew up in poverty. His mother was addicted to drugs and young Floyd would often find syringes around home. As for Floyd's father, when not boxing he also sold drugs to provide for his family.
Conor McGregor's experience with poverty was self-inflicted. After quitting his job as a plumber, Conor had no money coming in while he trained to be an MMA fighter. As a result, McGregor was a welfare recipient in Ireland just a few years shy of breaking out into superstardom. As a result of his government's support of him while training, Conor has said he always tries to pay back his home country as best he can.
If Conor McGregor and Floyd Mayweather weren't rivals they might actually be friends. The two have several things in common, including their love of exotic cars.
Conor is actually taking his love of exotic cars into a business. McGregor has recently partnered up with HR Owen to begin importing exotic luxury cars into Ireland for purchase. Naturally, many Irish fans have pointed out that few in the country would be able to purchase such expensive vehicles. Perhaps Conor figures that him fighting Floyd and then spending the money he earns in Ireland, the entire GDP of the country will be impacted, allowing more Irish to purchase such cars.
In January of 2015, Floyd tweeted out a photo of eight of his luxury cars he keeps, with experts estimating their combined worth at just under $6 million.
Floyd Mayweather should be an Olympic gold medalist. A 19-year-old Mayweather competed for the United States in the 1996 Olympic Games. The games were held in Atlanta that year, which was good for Mayweather considering he still has elected never to fight outside his home country as a professional.
In the semi-finals Mayweather appeared to have defeated Bulgarian boxer Serafim Todorov to advance to the gold medal bout. While the announcement was being read the referee raised Floyd's hand assuming he had won. The judges however, awarded the bout to the Bulgarian. The US team would file an official complaint, stating the judges were intimidated by the Bulgarian boxing coach, and that Floyd was not given credit for many punches landed. One of the American judges assigned to the games that year resigned in protest.
While Conor McGregor and Floyd Mayweather are similar in a lot of ways, there is one area of life in which they couldn't be farther apart.
Floyd Mayweather has a history of domestic abuse. On five different occasions, dating from 2002-10, Mayweather has been up on charges relating to domestic abuse or some type of incident with a girlfriend. Most recently a judge sentenced Floyd to 90 days in jail for an assault on former girlfriend Jodie Harris, as well as for stealing her phone. After legal proceedings were finished Floyd began serving his sentence in June 2012, and was released that August.
As for Conor, he is completely on the other side of the spectrum. The 28-year-old McGregor has been with the same woman since both were teenagers. Dee Devlin and Conor have been together for over 10 years, and Conor credits her with much of his success. The couple are expecting their first child together later this spring.
Dana White had no intentions of signing any fighters when he accepted an award in Dublin in 2013. White was in town to accept an award at Trinity College in Dublin, when he was bombarded by fans asking him to take a look at an up-and-coming Irish fighter named Conor McGregor.
White had so many people urging him to sign Conor that he asked some UFC employees to do some research into him. The rest is history, as the UFC ended up flying Conor into Las Vegas and signed him shortly after. He was signed before Dana White had actually sat down and watched a Conor McGregor fight himself.
Considering the amount of work Dana White has done over the years scouring the globe for new talent, it is interesting that the biggest star in the history of the company was someone he almost overlooked completely.
Perhaps the most surprising thing to occur during these crazy fight negotiations is that the UFC is actually willing to let this fight happen. Are they willing to do so for free? Probably not, in fact some are speculating the UFC is asking for as much as half of Floyd's purse for the bout.
Originally Dana White and the UFC had said they were the only promotion which could put on this bout, but that rhetoric has changed drastically recently. Now Dana White has told reporters that he, nor the UFC, would stand in Conor McGregor's way of making the kind of money he would by fighting Floyd. The only question now is how much of that money the UFC will get to keep for themselves.
Should Conor look bad in his bout with Floyd it could end up hurting his drawing power in the UFC. But if he shocks the world and beats Mayweather, he would end up bringing a large amount of fans from boxing back with him when he reappears in the UFC.


First Assembly of God Kiddie College is a family child care provider in Lewisburg, TN. First Assembly of God Kiddie College cares for children as young as 6 weeks through 12 years old. To learn more about this child care provider, please send them an email.
Little Tikes Day Care II, Inc.


text:
Parrjazz presents Frank Griffith
Ma Boyle's Alehouse and Eatery Tower Gardens Start Date - 5 Feb 2022 End Date - 5 Feb 2022 20:30pm
About this Event - Parrjazz presents Frank Griffith
Originating from the West Coast, renowned Saxophonist, Clarinetist and Arranger, Frank Griffith developed his distinctive New York jazz sound living and performing in the city for over 20 years before moving to London, meeting and playing with one of his great influences Sir John Dankworth.
Frank has performed with musicians such as Ron Carter, Jon Hendricks, John Pizzarelli, Joe Temperley, Pete Cater, Mel Torme, Dame Cleo Laine, Tony Coe and Kenny Wheeler. Frank has achieved great acclaim as an arranger, composing for a number of well-known singers to include Tina May, Alexander Stewart, David Mcalmont, China Moses and Anita Wardel.
He has also been the musical director for a number of programmes to include Kind of Blue at Bridport Arts Centre, Jazz on a Summers Day, Dorchester Corn Exchange and The Billy Strayhorn story, Cadogan Hall, London, London Jazz festival. Counting Joe Henderson Lester Young, Duke Ellington and Burt Bacharach as some of his main influences, Frank plays many forms of jazz including modern, mainstream and traditional alongside funk,
soul and some crossover Classical.
Ma Boyle's Alehouse and Eatery Tower Gardens


The onset of fire season should be the hottest thing about interviewing smokejumpers for Whitney Storm—until she sees Tom MacKenzie. The firefighter set her heart aflame ten years ago, then disappeared. As an empath who doesn't need emotional turmoil, this six-foot tall dark and dangerous memory has no place in her life.


Being the smartest or the fastest doesnt get you much in God's book....Its howto live in a way most pleasing to God......I just dont get it.....the only way to get a sheeps attention is with a cattle prod...... maybe christians react the same too afterall we are people like others except we have laid our sins down before the God of heaven and faithfully trusted Him to wash them away. As I stop for a sec to gather my thoughts Im reminded to just watch as I walk, guard what comes from our lips....be quick to hear slow to speak and slow to wrath. Thank God redeemed!!!!!
You need to be a member of the hot spot to add comments!
You said, "My kids weren't perfect either." You also said that your wife said, "That's my son". Is this not your son too or is this your step-son?
Love you brother. This is a horrible situation they put us in. They take away our lives & force us to live theirs.
Yea, just going to rehab without physically staying at one isn't going to work. They need to go away to one & not to the same one. Rarely do 2 addicts make it work either. You need to keep those doors locked though for your own safety brother. Still praying.
Just hang in there brother. They still going to rehab?
Wow Chip. Sounds like kids are really putting you thru it. I have no clue what u going thru brother so I have absolutely no advice to give. Destiny has given us a tough time. We finally had to draw a hard line. She is now in rehab & told her she can't come home. She has to find housing at a sober living once she's finished there. She's grown & has to figure this thing out called life. At her age, I had 2 brand new houses already built. I know her first marriage was a failure which wasn't her doing, however, she did choose the loser of a husband. Her choices after that were her decisions though. Unfortunately, she drug us all along for that ride. You gonna have to cut that umbilical cord.
Those kids u talking about are shooting heroine. I praise the good Lord above the hardest thing I had to deal with her were Xenex & Pot. That has been tough enough. I couldn't imagine dealing with anything harder. Heroine is a tough one. You don't need that brother. This is the time you're suppose to be sitting back & enjoying the rest of your life. You've put in your time working. This is your time of relaxation. Keep their junk on the curve. It's tough but that's the only route that works or that's the only road that has put her on the straight & narrow thus far.
Thank you well I work 5 days a week as a Processor at Goodwill but I dont make quite enough to live by myself.I could use a roommate, another relationship , friends, placement family especially with mom in nursing home rehab after hospital with lung cancer.Im an only child, Ive forgiven her family but not forget.An aunt knows about this but I prefer to find a new family to turn to, too much hurt from real family.Loads of responsibilities little to no support.Mom wants to come home but shell only smoke behind my back and become dependent on me.I work though, I feel Im making right decision visiting her sometimes but making sure shes under 24 hr care.I am hoping shell recover from lung cancer through rehab.
Chip, I definitely feel your pain. You kinda wrapped up several issues & crossed them over each other but I know what you're saying.
That's funny Seek. It cracks me up when someone sends me a message & then messages me that they sent me a message.