text:
\section{Introduction}

A fundamental expectation of a quantum theory of gravity is that it will cure the problems
that plague classical general relativity. One hopes, for example, that singularities get resolved in quantum
gravity \cite{cm69,bb84,kr97,ymo00,bt06}, that quantum gravity will provide the theoretcial foundation for
cosmic censorship \cite{rp79} and that it will give a better understanding of the relationship, already
predicted on the semi-classical level, between gravity and thermodynamics \cite{sh71,jb72,bch73,sh75}.

In the absence of a generally agreed upon framework for such a theory, a useful approach is to quantize
simplified classical gravitational models using canonical techniques, in the expectation that this will
lead to new ways to look at some of the issues raised above while, at the same time, pointing to what one
may expect out of the full theory. In this spirit, we recently developed \cite{vaz10} a novel approach to
Hawking evaporation taking place during the collapse of a self-gravitating dust ball. This approach,
based on an exact canonical quantization of the non-rotating, marginally bound gravity-dust
system \cite{ltb}, exploited
the matching conditions that must be satisfied at the apparent horizon by the wave functionals describing
the collapse and differs from the traditional approach in which a pre-existing black hole
is imagined to be surrounded by a tenuous field and the Bogoliubov transformation of the field operators
is computed in the black hole background \cite{vksw02,kmsv07,fgk10}.

The geometrodynamic constraints of all LeMa\^\i tre-Tolman-Bondi (LTB) models in any dimension, with or
without a cosmological
constant, are expressible in terms of a canonical chart consisting of the area radius, $R$, the dust proper
time, $\tau$, the mass function, $F$, and their conjugate momenta \cite{vws01,tsv08}. After a series of
canonical transformations in the spirit of Kucha\v r \cite{kk94}, the Hamiltonian constraint can be shown
to yield a Klein-Gordon-like Wheeler-DeWitt equation for the wave-functional. This equation can be solved
by quadrature and, in the simplest cases, closed form solutions can be obtained after regularization is
implemented on a lattice in a self-consistent manner. Self-consistency requires that the lattice
decomposition is compatible with the diffeomorphism constraint \cite{kmv06}. In these models, the dust
ball may be viewed as being made up of shells and the wave functional is described as the continuum limit
of an infinite product over the shell wave functions.

For the special case of marginal collapse with a vanishing cosmological constant in 3+1 dimensions, the
Wheeler-DeWitt equation can be solved explicity. We showed in \cite{vaz10} that matching the shell
wave-functions across the apparent horizon requires ingoing modes in the exterior to be accompanied by
outgoing modes in the interior and, vice-versa, ingoing modes in the interior to be accompanied by outgoing
modes in the exterior. In each case the relative amplitude of the outgoing wave is suppressed by the square
root of the Boltzmann factor at a ``Hawking'' temperature given by $T_H=(4\pi F)^{-1}$, where $F$ represents
twice the mass contained within the shell. Thus the temperature varies from shell to shell, decreasing from
the interior to the exterior, but it has the Hawking form for any given shell.

Two separate solutions are possible: one in which there is a flow of matter toward the apparent horizon both in
the exterior and in the interior, and another in which the flow is away from the horizon, again in both regions.
Matter undergoing continual collapse across the apparent horizon is described by a linear superposition of these
solutions and then, because ingoing waves in the interior are accompanied by outgoing waves in the exterior, the
horizon appears, to the external observer with no access to the interior, to possess a reflectivity given by the
Boltzmann factor at the above Hawking temperature. A different interpretation is also possible when the entire
shell wave functions are taken into account. Ingoing waves in the exterior must be accompanied by outgoing waves
in the interior, whose amplitude is also suppressed by the square root of the Boltzmann factor at the Hawking
temperature.  We showed that the transmittance of the horizon is unity, whether for waves incident from the
exterior or the interior. Thus this outgoing wave in the interior passes through the apparent horizon unhindered
but, because its amplitude is suppressed by the Boltzmann factor at the Hawking temperature relative to the
ingoing modes in the exterior, the emission probability of the horizon is given by the same factor. The net
effect is therefore reminiscent of the quasi-classical tunneling of particles through the horizon in the
semi-classical theory \cite{kw95,sp99,gv99,pw00,mp04}.

The solutions just described relied on explicit solutions for the shell wave functions. These are available
only in the case of the marginal models with a vanishing cosmological constant. Our aim here is to extend
these results to non-marginally-bound LTB models in arbitrary dimension with a negative cosmological constant.
No explicit solutions can be given in this case. Nevertheless, we will show that the results mentioned in the
previous paragraphs are indeed generic and that they are a consequence only of the essential singularity of the
Klein-Gordon equation for shells at the apparent horizon. We will then discuss how diffeomorphism invariant
wave functionals may be reconstructed out of the shell wave functions. Hawking radiation from the apparent
horizon then appears as a consequence of the generic form of the Wheeler-DeWitt equation describing
dust collapse and not of any particular solution disucssed in the earlier work. This will provide a novel way
to compute the entropy of the final state black hole.

The plan of this paper is as follows. In section II we recall some key results for classical dust collapse
with a negative cosmological constant in arbitrary dimensions. In section III we present the exact wave
functional that is factorizable on a lattice and solves the Wheeler-DeWitt equation for dust collapse.
The (collapse) wave functional can be thought of as an
infinite product of shell wave functions, each occupying a lattice site. Matching shell wave functions across
the horizon by analytic continuation in section IV, we argue that ingoing waves in one region must be
accompanied by outgoing waves in the other. We superpose the two solutions to conserve the flux of shells
across the horizon and then reconstruct the wave functional from the shell wave functions by going to the
continuum limit. A consequence of matching shells across the apparent horizon is that the amplitude for
outgoing waves relative to ingoing ones is given by $e^{-S/2}$, where $S$ is the Bekenstein-Hawking entropy of the final state black hole.
We close with a brief discussion of our results in section V.

\section{Non-Marginal Dust collapse with $\Lambda\neq 0$ in $d$ Dimensions}

\subsection{The classical models}

Let us begin by briefly recalling some pertinent facts about spherical dust collapse in the presence of a
negative cosmological constant (see, for example, \cite{tgsv08} for details). The LTB models describe self-gravitating
time-like dust whose energy momentum tensor is $T_{\mu\nu} = \varepsilon(x) U_\mu U_\nu$, where $U^\mu(\tau,\rho)$
is the four velocity of the dust particles which are labeled by the $\rho$ and with proper time $\tau$. The line
element can be taken to be
\begin{equation}
ds^2 = -g_{\mu\nu} dx^\mu dx^\nu = d\tau^2 - \frac{R'^2(\tau,\rho)}{1+2 E(\rho)}d\rho^2+R^2(\tau,\rho)d\Omega_n^2
\label{ltbmetric}
\end{equation}
where $R(\tau,\rho)$ is the area radius, $E(\rho)$ is an arbitrary function of the shell label coordinate,
called the energy function, and $\Omega_n$ is the $n=d-2$ dimensional solid angle. Einstein's equations
in the presence of a negative cosmological constant, which we call $-\Lambda$,
\begin{equation}
G_{\mu\nu} + \Lambda g_{\mu\nu} = - \kappa_d T_{\mu\nu},
\end{equation}
yield one dynamical equation for the area radius,
\begin{equation}
{R^*}^2 = 2E(\rho) + \frac{F(\rho)}{R^{n-1}}-\frac{2\Lambda R^2}{n(n+1)},
\label{rdoteq}
\end{equation}
where the star refers to a derivative with respect to $\tau$ and $F(\rho)$ is a second arbitrary function of the
shell label coordinate, called the mass function. Above, $\kappa_d$ is given in terms of the $d-$dimensional
gravitational constant $G_d$ as $\kappa_d = 8\pi G_d$.

One also finds the energy density,
\begin{equation}
\varepsilon(\tau,\rho) = \frac n{2\kappa_d} \frac{{\widetilde F}}{R^n {\widetilde R}},
\label{energydensity}
\end{equation}
in terms of $F$, where the tilde refers to a derivative with respect to the label coordinate, $\rho$. Specific
models are obtained by making choices of the mass and energy functions. For the solutions of \eqref{rdoteq}
to describe gravitational collapse (as opposed to an expansion) one must impose the additional condition that
$R^*(t,r)<0$. The solutions to \eqref{rdoteq} have been explicitly given in \cite{tgsv08} and analyzed in
detail for the marginally bound case, $E(\rho)=0$. Each shell reaches a zero area radius, $R(\tau,\rho)=0$,
in a finite proper time, $\tau=\tau_s(\rho)$, which leads to a curvature singularity. Thus the proper time parameter lies in the interval $(-\infty,\tau_s]$. In general both naked singularities and black hole end states can form.

Trapped surfaces occur when
\begin{equation}
{\mathcal F}~ \stackrel{\text{def}}{=}~ 1-\frac F{R^{n-1}} + \frac{2\Lambda R^2}{n(n+1)} = 0,
\end{equation}
which determines the physical radius, $R_h$, of the apparent horizon. ${\mathcal F}$ is positive outside, {\it i.e.,}
when $R>R_h$, and negative inside, when $R<R_h$.

\subsection{The Canonical Formulation}

To develop a canonical formulation of the LTB models, one begins with the spherically symmetric
Arnowitt-Deser-Misner (ADM) metric
\begin{equation}
ds^2 = N^2 dt^2 - L^2 (dr+N^r dt)^2 - R^2 d\Omega_n^2,
\end{equation}
where $N(t,r)$ and $N^r(t,r)$ are, respectively, the lapse and shift functions and the Einstein-Hilbert
action for a self-gravitating dust ball
\begin{equation}
S_\text{EH} = \frac 1{2\kappa_d} \int d^d x \sqrt{-g} ({}^d{\mathcal R} + 2\Lambda) -\frac 12 \int d^d x\sqrt{-g}
(g_{\alpha\beta} U^\alpha U^\beta +1),
\end{equation}
where $U_\alpha=-\tau_{,\alpha}$ for non-rotating dust, whete $\tau$ is the dust proper time. The phase space
consists of the dust proper time, $\tau(t,r)$, the area radius, $R(t,r)$, the radial function, $L(t,r)$, and
their conjugate momenta, respectively $P_\tau(t,r)$, $P_R(t,r)$ and $P_L(t,r)$.

When the ADM metric is embedded in the spacetime described by \eqref{ltbmetric} it becomes possible, through
a series of canonical transformations described in detail in \cite{tsv08}, to re-express the canonical constraints
in terms of a new canonical chart consisting of the dust proper time, the area radius and the mass density function,
$\Gamma(r)$, defined by
\begin{equation}
F(r) = \frac{2\kappa_d}{n\Omega_n}\left[M_0 + \int_0^r \Gamma(r') dr'\right]
\label{massdensity}
\end{equation}
and new conjugate momenta, $P_\tau(t,r)$, ${\overline P}_R(t,r)$ and $P_\Gamma(t,r)$.  The energy function is
expressible in this chart as
\begin{equation}
\frac 1{\sqrt{1+2E}} = \frac{2P_\tau}\Gamma
\end{equation}
and the transformations also absorb a boundary term, which is present in the original chart. The constraints
for the dust-gravity system in any dimension are
\begin{eqnarray}
{\mathcal H}^g &=& P_\tau^2 + {\mathcal F} {\overline P}_R^2 -\frac{\Gamma^2}{{\mathcal F}} \approx 0\cr\cr
{\mathcal H}_r &=& \tau'P_\tau + R' {\overline P}_R -\Gamma P_\Gamma' \approx 0,
\label{constraints}
\end{eqnarray}
where the prime denotes a derivative with respect to the ADM label coordinate, $r$. The Hamiltonian constraint
in \eqref{constraints} will be seen to contain no derivative terms, which makes it easier to quantize.
However, the Poisson brackets of the Hamiltonian with itself vanishes, indicating that the
Hamiltonian constraint does not generate hypersurface deformations. Rather, the transformations generated
by the Hamiltonian constraint act along the dust flow lines.

Of importance in what follows will be the following relationship between the dust proper time and the
remaining canonical variables (see, for example, \cite{vgks07})
\begin{equation}
\tau' = \frac{2P_\Gamma'}a \pm R' \frac{\sqrt{1-a^2 {\mathcal F}}}{a{\mathcal F}},
\end{equation}
where $a = 1/\sqrt{1+2E}$.\footnote{Einstein's equations guarantee that $1-a^2{\mathcal F} >0$ for $0<a<1$,
which corresponds to the case $E>0$.} The positive sign describes a collapsing dust cloud in the exterior
and an expanding dust cloud in the interior whereas the negative sign describes an expanding cloud in the exterior and a collapsing cloud in the interior. Integrating on a hypersurface of constant $t$ we have
the formal solution
\begin{equation}
\tau = 2\int_{t=\text{const.}} \frac{dP_\Gamma}a \pm \int_{t=\text{const.}}^R dR \frac{\sqrt{1-a^2 {\mathcal F}}}
{a{\mathcal F}} + \widetilde{\tau}(t),
\label{pt}
\end{equation}
where $\widetilde{\tau}(t)$ is undetermined. This integral can be difficult to solve for arbitrary ($r$
dependent) mass and energy functions, but when they are both constant beyond some boundary, $r_b$, then
the solution may be expressed as
\begin{equation}
a\tau = 2P_\Gamma \pm \int^R dR \frac{\sqrt{1-a^2{\mathcal F}}}{\mathcal F} + \widetilde{\tau}(t).
\label{ptforsads}
\end{equation}
In this case we are dealing with the static Schwarzschild-AdS geometry for which $2P_\Gamma$ may be associated
with the Killing time \cite{kk94}, so \eqref{ptforsads} gives the relationship between Schwarzschild-AdS and
Painlev\'e -Gullstrand time \cite{mp01}. Solutions in the absence of a cosmological constant have been given in
\cite{kmv06,vgks07}.

\section{Quantum States in A Lattice Decomposition}

When Dirac's quantization condition is used to raise the classical constraints to operator constraints, which
act on a wave functional, the Hamiltonian constraint turns into the Wheeler-DeWitt equation and the momentum
constraint imposes spatial diffeomorphism invariance on the wave functional. One sees that the second is solved
automatically by a wave-functional of the form
\begin{equation}
\Psi[\tau,R,F] = U\left[\int_{-\infty}^\infty dr \Gamma(r) {\mathcal W}(\tau(r),R(r),F(r))\right]
\label{wavefunctionaldef}
\end{equation}
provided that ${\mathcal W}$ contains no explicit dependence on $r$ and where $U:\mathbb{R} \rightarrow \mathbb{C}$ is
an arbitrary differentiable function of its argument.

The wave functional is factorizable on a lattice placed on the real line (eg., see \cite{vaz10}) if $U$ is
chosen to be the exponential map for then, taking the lattice spacing to be $\sigma$,
\eqref{wavefunctionaldef} can be written as
\begin{equation}
\Psi[\tau,R,F] = \lim_{\sigma\rightarrow 0} \prod_i \psi_i(\tau_i,R_i,F_i)
\end{equation}
where
\begin{equation}
\psi_i(\tau_i,R_i,F_i) = e^{\sigma\Gamma_i {\mathcal W}(\tau_i,R_i,F_i)}
\end{equation}
and we have used $X_i=X(r_i)$. Thus we can think of $\Psi[\tau,R,F]$ as an infinite product of shell wave
functions, each occupying a lattice site. Each shell wave function satisfies
\begin{equation}
\left[\hbar^2\left(\frac{\partial^2}{\partial\tau_i^2} + {\mathcal F}_i \frac{\partial^2}{\partial R_i^2} + A_i
\frac{\partial}{\partial R_i} + B_i\right) + \frac{\sigma^2\Gamma_i^2}{{\mathcal F}_i}\right]\psi_i = 0
\label{kgeqn}
\end{equation}
where $A_i=A(R_i,F_i)$ and $B_i=B(R_i,F_i)$ are functions capturing the factor ordering ambiguities
that are always present in the canonical approach. They can be uniquely determined by  requiring the
above equation to be independent of the lattice spacing; one finds the general positive energy
solutions \cite{tsv08}
\begin{equation}
\psi_i = e^{\omega_i b_i}\times\exp\left\{-\frac{i\omega_i}\hbar \left[a_i\tau_i \pm \int^{R_i} dR_i
\frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i}\right]\right\},
\label{shellwavefunctions}
\end{equation}
where $\omega_i = \sigma \Gamma_i/2$ and the factor $e^{\omega_i b_i}$ amounts to a normalization. Note that
shell ``$i$'' crosses the apparent horizon when
${\mathcal F}_i=0$, which is an essential singularity of the wave equation. From the shell wave functions in
\eqref{shellwavefunctions} one reconstructs the wave functionals with the ansatz \eqref{wavefunctionaldef}
and $U=\exp$ as
\begin{equation}
\Psi[\tau,R,\Gamma] = e^{\frac 12\int dr \Gamma b(F(r))}\times \exp\left\{-\frac i{2\hbar}
\int dr\Gamma\left[a(F(r))\tau\pm \int^R_{r=\text{const.}} dR \frac{\sqrt{1- a^2(F(r)){\mathcal F}}}
{\mathcal F}\right]\right\}\\
\label{collapsewavefunctional}
\end{equation}
where we have set $a(r)=a(F(r))$ and $b(r)=b(F(r))$ as is required for diffeomorphism invariance.

\section{Tunneling}

The wave-functions of the previous section are defined in the interior as well as the exterior of the
apparent horizon, but the Wheeler-DeWitt equation has an essential singularity at the apparent horizon along
the path of integration. In order to match interior to exterior solutions, it is necessary to deform the path
in the complex $R$-plane. The direction of the deformation is chosen so that positive energy solutions decay.
While this deformed path does not correspond to the trajectory of any classical particle it represents a
tunneling of $s$-waves across the gravitational barrier represented by the apparent horizon. This is analogous
to the quasi-classical tunneling approach employed in semi-classical analyses \cite{kw95,sp99,gv99,pw00,mp04}.

\subsection{Shell Wave Functions}

From the expression for the phase in \eqref{shellwavefunctions},
\begin{equation}
{\mathcal W}^{(\pm)}_i = \frac{\omega_i}\hbar \left[a_i\tau_i \pm \int^{R_i} dR_i \frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i}
\right],
\label{phase}
\end{equation}
the phase velocity of the $i^\text{th}$ shell wave function is given by
\begin{equation}
\dot R_i = \mp \frac{a_i {\mathcal F}_i}{\sqrt{1-a_i^2{\mathcal F}_i}}.
\end{equation}
Thus the positive sign in \eqref{phase} describes ingoing waves in the exterior (${\mathcal F}_i>0$), whereas it describes
outgoing waves in the interior (${\mathcal F}_i<0$) and, likewise, the negative sign describes outgoing waves in the
exterior and ingoing waves in the interior.

A closed form solution for the integrals appearing in \eqref{collapsewavefunctional} and \eqref{pt} cannot be
given when the mass function and/or the energy function and/or the cosmological constant are non-vanishing. We may
however analyze their properties near the apparent horizon in the following way. Noting that ${\mathcal F}_i = 0$,
equivalently $R_i=R_{i,h}$, is a singularity of the integral appearing in the phase, ${\mathcal W}_i$, we define the integral
by analytically continuing to the complex plane and deforming the integration path so as to go around the pole at
$R_{i,h}$ in a semi-circle of radius $\epsilon$ drawn in the upper half plane. Let $L_\epsilon$ denote the
deformed path and let $S_\epsilon$ denote the semi-circle of radius $\epsilon$ around $R_{i,h}$, then
\begin{equation}
\int^{R_i} dR_i \frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i}~ \stackrel{\text{def}}{=}~ \lim_{\epsilon
\rightarrow 0} {\int\limits_{L_\epsilon}}^{R_i} dR_i \frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i}.
\end{equation}
Performing the integration from left to right,\footnote{The same result is obtained if the integration
is performed from right to left.} for $R_i = R_{i,h}+\epsilon$ we have
\begin{equation}
{\int\limits_{L_\epsilon}}^{R_{i,h}+\epsilon}dR_i \frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i} =
{\int\limits_{L_\epsilon}}^{R_{i,h}-\epsilon}dR_i
\frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i} + \int\limits_{S_\epsilon} dR_i \frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i}
\end{equation}
and, for the integral over the semi-circle, a Laurent series expansion about ${\mathcal F}_i=0$ gives to lowest
order
\begin{equation}
\int_{S_\epsilon} dR_i \frac{\sqrt{1-a_i^2 {\mathcal F}_i}}{{\mathcal F}_i} = \frac 1{{\mathcal F}'_i(R_{i,h})} \int_{S_\epsilon}
\frac{dR_i}{R_i-R_{i,h}}.
\end{equation}
This integral is half the integral over a complete circle taken in a clockwise manner,
\begin{equation}
\int\limits_{S_\epsilon} dR_i \frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i}  = \frac 1{2{\mathcal F}'_i(R_{i,h})} \oint_{C_\epsilon}
\frac{dR_i }{R_i-R_{i,h}} = -\frac{i\pi}{2g_{i,h}},
\end{equation}
where $2g_{i,h} = {\mathcal F}'_i(R_{i,h})$ is the surface gravity of the horizon. Therefore we find
\begin{equation}
{\int\limits_{L_\epsilon}}^{R_{i,h}+\epsilon}dR_i \frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i} =
{\int\limits_{L_\epsilon}}^{R_{i,h}-\epsilon}dR_i \frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i} - \frac{i\pi}{2g_{i,h}}.
\end{equation}
The expression defining the proper time in \eqref{pt} involves a similar integral, but taken over a spatial slice.
Even so, the same argument can be made for this integral (see \cite{aas06,apgs09} for an analogous argument in the
semi-classical context). If we assume, moreover, that $a(F(r))$ and $P_\Gamma(r)$
are both regular across the horizon, the net result is that the phases in the exterior get matched
to the phases in the interior by the addition of a constant imaginary term,
\begin{equation}
{\mathcal W}_\text{out}^{(\pm)}(\tau_i,R_i,F_i) = {\mathcal W}_\text{in}^{(\pm)}(\tau_i,R_i,F_i) \mp \frac{i\pi\omega_i}
{\hbar g_{i,h}}.
\end{equation}
Thus we can give two independent solutions with support everywhere in the spacetime: an ingoing wave in the
exterior that is matched to an outgoing wave in the interior
\begin{equation}
\psi_i^{(1)}(\tau_i,R_i,F_i) = \left\{\begin{matrix}
e^{\omega_ib_i} \times \exp\left\{-\frac{i\omega_i}\hbar \left[a_i \tau_i + \int^{R_i} dR_i
\frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i}\right]\right\} & {\mathcal F}_i>0\cr\cr
e^{-\frac{\pi\omega_i}{\hbar{g_{i,h}}}}\times e^{\omega_ib_i} \times \exp\left\{-\frac{i\omega_i}\hbar
\left[a_i \tau_i + \int^{R_i} dR_i \frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i}\right]\right\} & {\mathcal F}_i < 0
\end{matrix}\right.
\end{equation}
and an outgoing wave in the exterior that is matched to an ingoing wave in the interior according to
\begin{equation}
\psi_i^{(2)}(\tau_i,R_i,F_i) = \left\{\begin{matrix}
e^{-\frac{\pi\omega_i}{\hbar{g_{i,h}}}}\times e^{\omega_ib_i} \times \exp\left\{-\frac{i\omega_i}\hbar
\left[a_i \tau_i - \int^{R_i} dR_i \frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i}\right]\right\} & {\mathcal F}_i > 0 \cr\cr
e^{\omega_ib_i} \times \exp\left\{-\frac{i\omega_i}\hbar \left[a_i \tau_i - \int^{R_i} dR_i
\frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i}\right]\right\} & {\mathcal F}_i < 0
\end{matrix}\right.
\end{equation}
The first of these solutions represents a flow towards the apparent horizon both in the exterior as well as
in the interior whereas the second represents a flow away from the apparent horizon in both regions.
While each solution is self-consistent, neither wave function accurately reflects the physical situation one
expects from semi-classical collapse, in which an ingoing shell proceeds all the way to the center and the
horizon emits thermal radiation into the exterior at the Hawking temperature.

To recover this picture we consider a linear superposition of the two wave functions
\begin{equation}
\psi_i = \psi^{(1)}_i + A_i \psi^{(2)}_i,
\end{equation}
where $A_i$ are complex valued constants. Following \cite{vaz10}, we fix these constants by requiring that
the current density is constant across the horizon. This implies that $|A_i|^2=1$ and we take $A_i=1$ for
every shell, which gives an absorption probability of unity for a shell to cross the apparent horizon from
the exterior. We therefore have
\begin{equation}
\psi_i = \left\{\begin{matrix}
\hskip -1.0in e^{\omega_ib_i} \times \exp\left\{-\frac{i\omega_i}\hbar \left[a_i \tau_i + \int^{R_i}
dR_i \frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i}\right]\right\} + & \cr
\hskip 1.0in +~ e^{-\frac{\pi\omega_i}{\hbar{g_{i,h}}}}\times e^{\omega_ib_i} \times \exp\left\{-\frac{i\omega_i}\hbar
\left[a_i \tau_i - \int^{R_i} dR_i \frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i}\right]\right\} & {\mathcal F}_i > 0 \cr\cr
\hskip -1.0in e^{-\frac{\pi\omega_i}{\hbar{g_{i,h}}}}\times e^{\omega_ib_i} \times \exp\left\{-\frac{i\omega_i}\hbar
\left[a_i \tau_i + \int^{R_i} dR_i \frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i}\right]\right\} + & \cr
\hskip 1.0in +~ e^{\omega_ib_i} \times \exp\left\{-\frac{i\omega_i}\hbar \left[a_i \tau_i - \int^{R_i} dR_i
\frac{\sqrt{1-a_i^2{\mathcal F}_i}}{{\mathcal F}_i}\right]\right\} & {\mathcal F}_i < 0
\end{matrix}\right.
\label{fullwavefunctions}
\end{equation}
The second term in the expression for $\psi_i$ in the exterior (${\mathcal F}_i>0$) is an outgoing wave that, to an external
observer, would represent a reflection with relative probability
\begin{equation}
\frac{P_{\text{ref},i}}{P_{\text{abs},i}} = e^{-\frac{2\pi\omega_i}{\hbar {g_{i,h}}}}.
\end{equation}
This is precisely the Boltzmann factor for the shell at temperature $T_{i,H}=\frac{\hbar {g_{i,h}}}
{2\pi k_B}$, where ${g_{i,h}}$ is the surface gravity of the apparent horizon.

This reflected piece is a purely quantum effect, necessitated by the
existence of an ingoing wave in the interior, {\it i.e.,} by requiring the continued collapse of the shell
beyond its apparent horizon. This continued collapse is represented by the second term in the expression
for $\psi_i$ in the interior (${\mathcal F}_i<0$). On the other hand, the ingoing wave in the exterior, represented
by the first term in the expression for $\psi_i$ when ${\mathcal F}_i>0$, is necessarily accompanied by an outgoing wave
in the interior occurring with a relative amplitude of $e^{-\frac{\pi\omega_i}{\hbar{g_h}}}$, which is
equal to the amplitude for ``reflection'' at the apparent horizon. This leads to the alternate picture
mentioned in the Introduction, in which the Hawking process can be viewed as an effective emission from
the apparent horizon.

\subsection{Phase Transition}

We can use our results above to examine what happens near the Hawking-Page Transition point \cite{hp83}.
It is worth noting that the Hawking temperature is independent of the energy function. This was first noted
in \cite{vgks07} in connection with non-marginal LTB models without a cosmological constant. Here we have shown
that the result is robust, holding even in the presence of a negative cosmological constant.

Now the apparent horizon is given for each shell as the solution of the equation
\begin{equation}
2x_{i,h}^{n+1} + n(n+1) x_{i,h}^{n-1} - n(n+1)F_i\Lambda^{\frac{n-1}2} = 0,
\label{hor}
\end{equation}
where $x_i = R_i\sqrt{\Lambda}$ is dimensionless, and it is straightforward to show that the surface gravity
for each shell is
\begin{equation}
{g_{i,h}} = \frac{\sqrt{\Lambda}}2\left[\frac{2x_{i,h}}n + \frac{n-1}{x_{i,h}}\right].
\label{surfgrav}
\end{equation}
For fixed $n$ and $\Lambda$,
\begin{equation}
\frac{d{g_{i,h}}}{dF_i} = \frac{\sqrt{\Lambda}}2 \frac{dx_{i,h}}{dF_i} \left[\frac 2n - \frac{n-1}{x_{i,h}^2}
\right],
\end{equation}
so using the fact that $dx_{i,h}/dF_i>0$, which follows directly from \eqref{hor}, we find that $d{g_{i,h}}/dF>0$
when $2x_{i,h}^2> n(n-1)$. This is the condition for positive specific heat. When $2x_{i,h}^2 < n(n-1)$ the
specific heat is negative and the two regimes are separated by the Hawking-Page (phase) transition \cite{hp83}, which
occurs at $2x_{i,h}^2=n(n+1)$. The wave functions of collapse in \eqref{fullwavefunctions} are
well behaved at the transition point.

\subsection{Wave Functionals}

We now turn to the question of how the collapsing shell wave functions described in the previous section may be combined
to yield wave functionals. Obviously the superposed wave functions of \eqref{fullwavefunctions} cannot be directly
used for this purpose as they are not the simple exponentials required for diffeomorphism invariance by
\eqref{wavefunctionaldef}. Instead, we take the continuum limit of the product of the shell wave functions
$\psi_i^{(1)}$ and $\psi_i^{(2)}$ separately to form two corresponding diffeomorphsim invariant wave functionals,
$\Psi_1$ and $\Psi_2$. Then, we take a linear combination of these wave functionals to form the full wave functional describing the collapse \cite{vaz10}	.

Accordingly, the functional equivalent of the superposed wave functions in \eqref{fullwavefunctions} is
$\Psi=\Psi_1+\Psi_2$, or
\begin{equation}
\Psi= \left\{\begin{matrix}
\hskip -0.5in e^{\frac 12\int dr \Gamma b} \times \exp\left\{-\frac i{2\hbar} \int^R dr \Gamma \left[a\tau +
\int_{r=\text{const.}}^{R} dR \frac{\sqrt{1-a^2{\mathcal F}}}{{\mathcal F}}\right]\right\} + & \cr\cr
\hskip 0.5in +~ e^{-S/2}\times e^{\frac 12\int dr \Gamma b} \times \exp\left\{-\frac i{2\hbar}
\int dr \Gamma \left[a \tau - \int_{r=\text{const.}}^R dR \frac{\sqrt{1-a^2{\mathcal F}}}{{\mathcal F}}\right]\right\} & {\mathcal F} > 0 \cr\cr\cr
\hskip -0.5in e^{-S/2}\times e^{\frac 12\int dr\Gamma b} \times \exp\left\{-\frac
i{2\hbar} \int dr \Gamma \left[a \tau + \int_{r=\text{const.}}^R dR \frac{\sqrt{1-a^2{\mathcal F}}}{{\mathcal F}}\right]\right\} + & \cr\cr
\hskip 0.5in +~ e^{\frac 12\int dr \Gamma b} \times \exp\left\{-\frac i{2\hbar}\int dr \Gamma \left[a \tau -
\int_{r=\text{const.}}^R dR \frac{\sqrt{1-a^2{\mathcal F}}}{{\mathcal F}}\right]\right\} & {\mathcal F} < 0
\end{matrix}\right.
\end{equation}
When use is made of \eqref{hor} and \eqref{surfgrav}, the relative amplitude, $e^{-\frac\pi{2\hbar}
\int dr \Gamma/{g_h}}$, works out to precisely $e^{-S/2}$, where $S=A_h/4\hbar G_d$ is the
Bekenstein-Hawking entropy of the black hole. Thus the ratio of the reflection probability to the
probability for absorption is determined only by the entropy of the black hole,
\begin{equation}
\frac{P_\text{ref}}{P_\text{abs}} = e^{-S}
\end{equation}
and we have recovered the results of \cite{vaz10} in the more general setting of $d-$dimensional, non-marginal
collapse and in the presence of a (negative) cosmological constant.

\section{Conclusions}

In this paper we have used the wave-functionals of an exact midi-superspace quantization of the
non-marginally-bound LTB models in the presence of a cosmological constant and in an arbitrary number of
spatial dimensions to study the Hawking evaporation process.  As in previous works, regularization was
performed on a lattice and the wave functionals were shown to be constructed out of wave functions
describing individual shells of collapsing dust. The apparent horizon is an essential singularity of
the Wheeler-DeWitt equation and the solutions of the latter could only be given by quadrature separately
in the exterior and in the interior of the apparent horizon. The central issue discussed here was how
the interior and exterior solutions can be matched across the horizon. To accomplish the required matching
we defined the integrals appearing in the solution of the Wheeler-DeWitt equation
by deforming the integration path in the complex plane to go around the pole at the apparent horizon. This
implied that crossing the horizon involved a rotation of the dust proper time in the complex plane and had
the effect of introducing an imaginary constant into the phase of the outgoing wave
functions. We were then able to show that an ingoing shell wave function in one region is required to be accompanied by an outgoing shell wave function in the other region. The relative amplitude of the outgoing
wave function in each case was shown to be given by the square root of the Boltzamann factor at the Hawking
temperature appropriate to the shell.

The approach in this paper enjoys several advantages over the approach via Bogoliubov coefficents, while also
producing an alternative and attractive view of the evaporation process. In the first place, no near horizon
expansion of the wave-functional is necessary. Secondly, the approach via Bogoliubov coefficients does not
get much beyond the semi-classical level because it is necessary to approximate the mass function in
such a way that it represents a massive black hole surrounded by tenuous dust. Hence one is effectively
looking at the semi-classical radiation from the event horizon of a static black hole. By contrast, no such
approximation to the mass function is necessary here, so we are genuinely examining the radiation from the
apparent horizon {\it during} collapse. Thirdly, the inner product used in the calculation of the Bogoliubov
coefficient is not the one that is uniquely determined by the lattice regularization (see Appendix B of
\cite{kmv06}) but one that is determined from the DeWitt supermetric. This can be justified only in
the approximation described above because, for this case alone, no measure is uniquely determined by the
regularization scheme \cite{vw09}). In all other cases, the measure is uniquely determined and different
from that provided by the DeWitt supermetric. The results we report here are independent of the inner product.

If the matter is assumed to undergo continued collapse we showed that the relative probability for the shell
wave function to cross the apparent horizon is unity, whether it is incident from the interior or the exterior.
This was argued to lead to two pictures of the evaporation process. In the first picture, one takes the point of
view of an external observer with no access to the interior. To this observer the horizon appears to possess a non-zero
reflectivity. On the other hand, the observer who has access to the entire wave function sees the outgoing
exterior portion of the shell wave function as a transmission of an outgoing interior wave across the horizon,
which exists because of the collapsing exterior. Thus the horizon can also be thought of as an emitter.

We showed that the Hawking temperature is independent of the energy function, {\it i.e.,} of the initial velocity
distribution of the shells, and that the shell wave functions are well behaved at the Hawking-Page transition
point during the collapse. Moreover, the relative amplitude for outgoing wave functionals is $e^{-S/2}$, where
$S$ is the Bekenstein-Hawking entropy of the final state black hole even in the presence of the cosmological
constant. This generalizes \cite{vaz10}, for which closed form solutions were available. The results are therefore
generic to dust collapse.
\bigskip\bigskip

\noindent{\bf Acknowledgements}
\bigskip

\noindent C.V. is grateful to T.P. Singh and to the Tata Institute of Fundamental Research
for their hospitality during the time this work was completed. K.L. and C.V. acknowledge useful conversations with
T.P. Singh and the partial support of the Templeton Foundation under Project ID $\#$ 20768.
\bigskip\bigskip

redpajama_set_name: RedPajamaArXiv


text:
Natrijum cijanid je natrijumova so cijanovodonične kiseline. Ovo jedinjenje ima hemijsku formulu -{NaCN}-. Na sobnoj temperaturi ova so je bezbojan kristalni prah, koji ima slab miris na gorke bademe. Veoma je higroskopana.

Dobijanje
Natrijum cijanid se dobija procesom neutralizacije cijanovodonične kiseline i natrijum hidroksida (sode) putem Andrusove reakcije. Za sintezu natrijum cijanida se koriste metan, amonijak i kiseonik.

Metan, amonijak i kiseonik reaguju na temperaturi od 1546 °-{C}- te uz prisustvo platine kao katalizatora dobija se voda i cijanovodonična kiselina.

Slijedi reakcija neutralizacije cijanovodonične kiseline i sode.

Cijanovodonična kiselina i soda daju natrijum cijanid i vodu.

Ranije se natrijum cijanid dobijao putem reakcije natrijuma sa ugljom i amonijakom.

Upotreba
Natrijum cijanid zajedno sa kalijum cijanidom se upotrebljava u proizvodnji plemenitih metala zlata i srebra. U galvanskoj tehnici se koristi u raznim cijanidnim kadama, npr. u cijanidnim kadama za bakar, mesing, bronzu, cink, kadmijum i zlato.

U organskoj hemiji natrijum cijanid se koristi u raznim sintezama. Natrijum cijanid je otrovan za ljude. Smrtonosna doza (oralno) iznosi oko 2,8 mg po kilogramu tjelesne mase.

Reference

Spoljašnje veze

Једињења натријума
Цијаниди

redpajama_set_name: RedPajamaWikipedia


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text:
Q: what is wrong with this SAX parsing and Xpath code? Working through Maven By Example, a book from quite a few years ago, but which is, I assume, retrieving the right versions from repositories, I'm just wondering what it going wrong with the unit testing in the first example.
We have an xml file, start thereof:
<?xml version="1.0" encoding="UTF-8" standalone="yes" ?>
<rss version="2.0" xmlns:yweather="http://xml.weather.yahoo.com/ns/rss/1.0" xmlns:geo="http://www.w3.org/2003/01/geo/wgs84_pos#">
 <channel>
 <title>Yahoo! Weather - New York, NY</title>
 <link>http://us.rd.yahoo.com/dailynews/rss/weather/New_York__NY/*http://weather.yahoo.com/forecast/10002_f.html</link>
 <description>Yahoo! Weather for New York, NY</description>
 <language>en-us</language>
 <lastBuildDate>Sat, 10 Nov 2007 8:51 pm EDT</lastBuildDate>
 <ttl>60</ttl>

 <!--************ THIS IS THE LINE WE'RE INTERESTED IN ************ -->
 <yweather:location city="New York" region="NY" country="US" />

 <yweather:units temperature="F" distance="mi" pressure="in" speed="mph" />

and this xml file is being read in via an InputStream and parsed:
    Weather weather = new Weather();
    log.info("Creating XML Reader");
    SAXReader xmlReader = createXmlReader();
    Document doc = xmlReader.read(inputStream);

    // this proves we're getting the text OK
    // String xml_text_content = doc.getStringValue();
    // log.info( "=== xml text content: |" + xml_text_content + "|" );

    log.info("Parsing XML Response");
    weather.setCity(doc.valueOf("/rss/channel/y:location/@city"));
    String city_str = doc.valueOf("/rss/channel/y:location/@city");
    // this should say "New York"... but I'm getting an empty string
    log.info( "=== doc value of for city: |" + city_str + "|" );

... I know very little about RSS and XPath, sorry.  Just seems like someone knowledgeable might see the problem!
PS I tried changing "yweather:location" to "y:location" in the xml file, and then "y:location" to "yweather:location" in the code... both threw exceptions.  Latter case:

528  INFO  YahooParser  - Parsing XML Response Tests run: 1, Failures:
  0, Errors: 1, Skipped: 0, Time elapsed: 0.096 sec <<< FAILURE!
  testParser(org.sonatype.mavenbook.custom.weather.yahoo.YahooParserTest)
  Time el apsed: 0.094 sec  <<< ERROR!org.dom4j.XPathException:
  Exception occurred evaluting XPath: /rss/channel/yweather:location/@city. Exception: XPath expression uses unbound namespace
  prefix yweather
          at org.dom4j.xpath.DefaultXPath.handleJaxenException(DefaultXPath.java:374)
              at org.dom4j.xpath.DefaultXPath.valueOf(DefaultXPath.java:185)
              at org.dom4j.tree.AbstractNode.valueOf(AbstractNode.java:191)
              at org.sonatype.mavenbook.custom.weather.YahooParser.parse(YahooParser.j
  ava:28)
              at org.sonatype.mavenbook.custom.weather.yahoo.YahooParserTest.testParse
  r(YahooParserTest.java:36)

"unbound namespace prefix yweather"...??? <gulp!>

A: The following code works for me:
import java.io.File;

import org.dom4j.Document;
import org.dom4j.DocumentException;
import org.dom4j.io.SAXReader;

public class TestSax {

    public static void main(String[] args) throws DocumentException {
        SAXReader xmlReader = new SAXReader();
        Document doc = xmlReader.read(new File("D:/Temp/sax.xml"));
        String city_str = doc.valueOf("/rss/channel/yweather:location/@city");
        System.out.println( "=== doc value of for city: |" + city_str + "|" );
    }
}

I took dom4j and required jar jaxen from here. Check if you use the same libraries.
Also note that I changed in code y:location to yweather:location.

A: Just putting in the solution (which worked for me) in case any readers of the same book have the same problem.
On page 38 (in my edition) - section 4.3 "Creating the Simple Weather Project", we are told to run this command:

$ mvn archetype:generate -DgroupId=org.sonatype.mavenbook.custom
  DartifactId=simple-weather -Dversion=1.0

On my system (Windows 7) this created the wrong directory structure: under "main" and under "test" there was a "spurious" directory under  "mavenbook": "custom".
On page 43, when you start creating the "main" and "test" directory structures, it will be obvious to cleverer people than me that this "custom" directory shouldn't be there...
My solution (which I arrived at finally) was indeed to get rid of this "custom" directory, make sure the paths matched OK in the import statements of the xxxxTest classes, and finally to make sure the parent pom.xml was in the same directory as directory "simple-weather" (the project pom.xml is in the latter directory).
It is also possible to download the project ready-built (as it's meant to be, without the "custom" directory) as explained in the book...
PS I feel it's worth the effort - if your builder/tester app doesn't work as expected where do you go from there?
PPS It's also worth the effort in that Maven does appear to be very well-designed and powerful...

A: replying to old post just incase someone wanting to know the solution (like me) I agree with custom folder issue above however it missing the actual solution to XPath issue.
book has
private SAXReader createXmlReader() {
Map<String,String> uris = new HashMap<String,String>();
uris.put( "y", "http://xml.weather.yahoo.com/ns/rss/1.0" );

changing the hash key to 'yweather' and Xpath to yweather:location (in code wherever y: should be yweather:....) as above in comment will work
uris.put( "yweather", "http://xml.weather.yahoo.com/ns/rss/1.0" );

redpajama_set_name: RedPajamaStackExchange


text:
Giant Freakin Robot > Entertainment
A New Star Wars Movie Short Was Just Released Online, Watch It Here
By Drew Dietsch | 4 months ago
A new Star Wars short has dropped online and it is one of the more exciting pieces of Star Wars filmmaking we have gotten in a while. The short film, called "Hunted", ties in with the new video game Star Wars: Squadrons and it promises some pretty thrilling possibilities.
Check out the new Star Wars short right here:
The Star Wars short film begins over a brand new planet called Var-Shaa, where an Imperial dockyard hovers in orbit. After the crucial events that took place during the Battle of Endor, the dockyard was attacked by the Rebel Alliance and only the Star Destroyer Overseer was left. The seven-minute short follows the story of an Imperial pilot named Varko Grey, the leader of a team of pilots known as Titan squadron, as he is struggling to survive the onslaught.
What is interesting about this new short film is how it frames the story from the perspective of an Imperial officer. While that certainly isn't uncommon in a lot of Star Wars material that isn't the main film series, it is still refreshing to get a story set from a viewpoint we don't get to see a lot of in the movies.
On that same note, the new character of Varko Grey certainly seems like a fascinating protagonist. Grey believes in the order that the Empire brought to the galaxy, and he is now stuck right in the middle of its precipitous downfall. Grey was originally a police officer on the planet Parkella, but became a TIE pilot after seeing the many sacrifices made by the brave Imperial soldiers in battle. Although Grey would come into conflict with the Empire's methods, his quest to prevent corruption and injustice saw them as the best hope for the galaxy.
Star Wars: Squadrons will have players alternating between New Republic and Imperial pilots in the campaign mode. Varko Grey is likely going to be one of the game's main protagonists. The story of the game involves an endeavor from the New Republic called Project Starhawk, and the Empire has sent spies to investigate the mysterious initiative.
There certainly seems to be a lot of momentum in the Star Wars universe. A potential new Mace Windu project is making the rumor rounds, and the new season The Mandalorian starts at the end of October. Star Wars: Squadrons is already available for pre-order and will release on October 2. It has been nine months since Star Wars: Episode IX – The Rise of Skywalker and four months since the ending of Star Wars: The Clone Wars. Looks like the Star Wars machine is getting back up and running.
Will we be getting a similar film that shows us the New Republic's side of things? This is obviously the beginning of a big ramp up for the game's advertising. Could we be getting a few more peaks into these new characters? And will we be seeing any other familiar faces from the Star Wars universe making an appearance? We'll find out once the game hits shelves at the beginning of October.
Disney Plus Shows Coming Soon: Donald Glover Returns As Lando
Upcoming Star Wars TV: We're Getting A New Star Wars Holiday Special
Kennedy And Favreau Battling For Control Of Star Wars In A Lucasfilm Civil War
See Millie Bobby Brown As Princess Leia

redpajama_set_name: RedPajamaCommonCrawl


text:
By Jim Parker
Published July 1, 2020 10:26 AM
Identities released for most victims in deadly El Paso crash after Border Patrol chase; 5 from Guatemala
Scene of a car crash along Paisano in downtown El Paso that killed 7 people.
EL PASO, Texas — El Paso police on Wednesday released the identities for most of the seven people killed and three injured when a car that had been pursued by the U.S. Border Patrol crashed in downtown last week.
Five of the ten victims, according to police, were from Guatemala.
The identities as well as ages and nationalities of the victims are as follows:
Driver: 18 –year old Gustavo Cervantes (deceased) of El Paso
Passenger 1: 21-year old Oscar Miguel Garcia-Bran (deceased) of Guatemala
Passenger 2: 19 –year old Elvira Tot-Chiroy (deceased) of Guatemala
Passenger 3: 16 –year old Liliana Jimenez, El Paso resident (deceased)
Passenger 4: 19 –year old tentative ID, El Paso resident (deceased) pending next of kin
Passenger 5: 16- year old Yadira Barrera El Paso resident (deceased)
Passenger 6: 32-year old Santos Porfirio-Garcia, (deceased) of Guatemala
Passenger 7: 16 –year old male of Juarez, Chih., MX
Passenger 8: 18 –year old Omar Misael Coyoy of Guatemala
Passenger 9: 25 –year old Wilmer Gomez-Gomez of Guatemala
A police spokesman noted that "any discrepancies in names and/or
nationalities listed on the initial release are due to fraudulent identification(s) found on the bodies of the deceased, or information provided by the injured."
The Border Patrol has said in a prior statement that the four-door sedan carrying the ten people was being chased because agents believed it was involved in a human smuggling effort, a claim that some of the victims' families have questioned.
The crash following that chase, at 2:15 a.m. last Thursday near the intersection of Paisano Street and San Antonio Avenue, is believed to be one of the deadliest in El Paso history.
Jim Parker
Jim Parker is the Director of Digital Content for ABC-7.
Excuse the typo: Cowboys botch Vander Esch's name on jersey
markturner1961 says:
Needless tragedy and very sad. Kid driver thinking he was bullet proof like most kids and BP officers acting irresponsibly.
uvacowboy says:
How is this the Border Patrol's fault. This is a sad story but they broke the law. What was the Border Patrol supposed to do? Turn a blind eye?
Fero2A says:
Libtards like markturner aka Alberto always blame the Border Patrol or other law enforcement instead of the root cause. His main problem is lack of intelligence.
Nobody is saying it was the fault of the BP. I'm saying they acted irresponsibly. Evidently the BP supervisors agree.
You are wrong. The CBP officers acted within the law with probable cause. The kid was probably looking at the making money aspects of being an illegal human smuggler. He wasn't too smart either. You don't cram 10 people into a compact car and do high speeds on downtown city streets.
Steve on Resler says:
Mark Turner, you're an idiot. Whoever was driving a compact car that was easily double over occupancy was irresponsible. Just because you hate law enforcement doesn't mean they're wrong all the time. Quit making shit up or back it up with facts
I've always supported law enforcement on this blog and you damn well know it. They screwed up in this instance and you know that too.
K1DPR says:
Now, DEPORT THE SURVIVORS!
truthofthematter says:
MORE smuggling s.h.i.t ought to end this way! F..k EM!
Find whoever set this up, charge them with murder. You know a bunch of kids didn't set this all up.
Hard to find and prove it, but if they can, fry 'em.
What needs to happen is complete overhaul of the immigration system so these kinds of things won't have a chance or reason to occur.
Yeah, secure the god-damned border!


After several years of being iPad-only for the majority of my work, I often take some of these features for granted. And admittedly, Apple doesn't always do a great job at teaching users about these lesser known details, which have become especially important after the productivity-focused iPad update in iOS 11. I hope this collection can be useful for those who haven't yet explored the fascinating world of iPad productivity.
Eine tolle Sammlung von Tipps zur Arbeit auf dem iPad. Vor allem der erste Tipp, den Federico bereits vor einiger Zeit in einer Connected-Folge erwähnt hatte, war eine Erleuchtung für mich! Seither kann ich endlich handschriftliche Notizen aus Apple Notes mit meinen OmniFocus-Tasks verbinden.


What are the 'to be' verbs in present tense in french?
The transport system of the body responsible for carrying oxygen and nutrients to the body and carrying away carbon dioxide and other wastes; composed of the heart, blood vessels, and blood.
Who was Martin Luther and what did he do?
The creator of the reformation, he broke away from the Catholic Church and created the Lutheran Church. He also questioned the Pope's role in the church and the sale of indulgences. He's also known for the 95 theses.
needs and Thelma will reply soon.


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Q: Signing Identity dropdown list is empty after upgrading Visual Studio 2019 on Windows platform Building iOS apps with Xamarin.Forms on Windows using Visual Studio is real struggle. Every single day I have endless weird problems...
I've successfully distributed an app yesterday. Today I cannot sign the archive anymore because the Signing Identity dropdown list is empty:

I download all the profiles at Project Properties page:

My older archives are lost either. I hate those minor VS updates; many of them larger than GBs and cause conflicts when you develop at more than one machine plus Mac device.
How can get the identity back that I've downloaded?
P.S: Removing & re-adding the Apple account didn't work. I could rebuilt,re-archived and then distributed using other pc. Notice the Signing Identity, it's not automatic this time.

A: *

*Go to Tools > Options > Apple Accounts

*Add your Apple ID and validate.

*Scroll Down there is a list of your teams

*Select one and go to "View Details"

*Here you can add certificates and download profiles, or import them from your Mac key chain.

*Go to the bundle signing section and select the correct profile.


Here is what we did on Monday.
Math: Today we explored angles in quadrilaterals! We talked about how squares and rectangles have 4 equal angles, parallelograms and rhombuses have opposite equal angles and lastly all kites have 2 equal angles. To show that angles are equal you draw matching arcs. We did examples on the board and a few textbook questions for practice.
Language: We started our new novel study. We are reading the famous novel, "The Secret Garden." The students are so excited to begin a new story adventure! They made so many connections to our last novel study book as well.
UOI: We completed our soil experiment! We drew out the last stage of the experiment. Today we also learned about the different layers of soil. We watched a video and discussed what is included in each layer.


This is truth; this is spiritual food. But so many Christians live their lives blind to this light of God. The word hell comes from an ancient Germanic word meaning place covered over, not a place of eternal torment. It is a life where we cover ourselves so as to block out Gods light – the promised land, allegorically speaking. And too many Christians live just like that – in the hell of this life blind to God. This is the root of fear. I did myself for many years until the scale came off my eyes. God bless you Jacob and thanks.
our lives. Reveltion is our meat and the truth it brings is our drink. Let no man..no man judge you. For God is our Judge. This means God has from the beginning set before man what is right and what is wrong. No man has the wherewithal to do such a thing, ask Job.
I am always so grateful to God when I open up my email and find your message. The power that is revealed in a few minutes breaks forth so much truth. Like the other viewers your messages are always for the hour. I watched your video with my daughter who has been going through with some terrible challenges of being of fear of not knowing how her personal, job and just fear in general. She and I got free at the same time together while watching God move through you. Wow, in less then 14 minutes!!!
Perfect love cast out all fear, 1John 4:18. Thank you so much Jacob.
I send your messages out to my family and friends on facebook. You have a following, my friend. They ask me all the time where is he? You keep beign faithful your rewards are in heaven but many of us are being set free on earth from the religious blindness. Christ in us is our hope of Glory! And in regards to that tee shirt…it would not be a back idea. Keep the words of God fresh and keep opening your mouth telling the truth!!! Thank you for your love and kindness Jacob.
there is no fear in love, love will take care of it all. don't be fearfull god has it all fixed just believe.
God bless you brother!! Wonderful and encouraging teaching.
Thanks Diane! God Bless and Keep you too!


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Southeast Tennis & Learning Center Celebrates 25 Years!
It's call the Southeast Tennis and Learning Center. But the sprawling facility is about so much more than rackets, nets and tennis balls. It is an educational haven for children in DC's Southeast community. There's no promise that the thousands of children who have been served by the center will be come tennis champions… but they will come out, changed for the better. We talk about the past 25 years of the center and The Recreation Wish List Committee.
Southeast Tennis & Learning Center Gala Info
Southeast Tennis & Learning Center/Twitter
http://whur.com/wp-content/uploads/2019/10/THE-DAILY-DRUM-10.22.19-SOUTHEAST-TENNIS-AND-LEARNING-CTR.mp3
Justice Bobbitt, Director, The Southeast Tennis & Learning Center (not pictured)
Cora Masters Barry, Former First Lady of The District of Columbia, Founder, The Southeast Tennis & Learning Center, The Recreation Wish List Committee
Tags: Cora Masters-Barry, Former First Lady of The District of Columbia, Justice Bobbitt, tennis, The Recreation Wish List Committee, The Southeast Tennis & Learning Center
Venus Williams Falls To Coco Gauff in Aussie Open


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UFC Vegas 41: Costa vs. Vettori
Cormier accuses referee of reading too many 'headlines,' being 'too fast' to punish Paulo Costa
Daniel Cormier feels referee Jason Herzog allowed himself to be affected by the narrative against Paulo Costa ahead of UFC Vegas 41.
By Milan Ordoñez@Mr_Ordonez Oct 26, 2021, 4:38am EDT
Share All sharing options for: Cormier accuses referee of reading too many 'headlines,' being 'too fast' to punish Paulo Costa
Paulo Costa caused quite a stir on fight week leading up to his Saturday headliner against Marvin Vettori at UFC Vegas 41. "Borrachinha" was unable to make the supposed middleweight limit, forcing the bout to be moved to a 195-pound catchweight, and eventually, to a light heavyweight contest.
This put Costa in a negative light. Former fighters who've gone through the same situation in the past called him out for being "lazy."
That narrative against Costa may have carried over to the fight and affected referee Jason Herzog's judgment, at least according to Daniel Cormier. The former UFC double-champ questioned the official's decision to immediately deduct a point on the Brazilian fighter for his inadvertent eye poke on Vettori in round two.
"The poke in the eye, I get it. But, when he got a point deducted — and I'll tell you this, I thought this immediately right after. I thought to myself, 'Jason Herzog has been watching the headlines.' Jason Herzog has been watching and paying attention to the story that's going around this fight," Cormier said in a recent video from his YouTube channel.
"Because everybody hates Costa, from the weigh-in, he's like, rubbing his hands, he's, like, playing the bad guy all week. But when (Herzog) took the point after one eye poke? That really did not look intentional to me.
"It told me that Herzog has been kind of following the headlines, and he allowed for that emotion of Costa being the bad guy to make him go a little bit too fast.
"Should've been a warning. We have seen much more severe eye pokes happen in fights. I've done them myself where I've poked guys more than this guy poked Marvin Vettori. And then get a point taken away."
Cormier went on to point out how it's seemingly a norm to pay attention to the headlines and how it could affect certain decisions.
"As an official, you can't read the headlines," he said. "That's one thing that I've learned as I've been doing these fights. Everybody pays much more attention than you ever want to believe. Everybody, from the fighters to the referees, everybody pays attention. The commentators. Everybody listens.
"And they listen to things that they shouldn't, so at times, as humans, they make decisions — or we make decisions that may end up not being the right thing for the situation. And I think in this one, Herzog read the headlines and he may have judged Costa unfairly."
Costa ended up losing the fight via decision. He also had to give up 20 percent of his purse for his weight miss.


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Tag Archives: Royston Vasey
City & Country, Country Walks Without a Car, Walking
Hilary Mantel on the Pseudonymonous Hadfield, with a reservoir walk
April 3, 2018 Andrea Gibbons	Leave a comment
I read, and loved, Hillary Mantel's Fludd over the Christmas holidays, after finding it on a shelf in the Inverness cottage where we were staying. I copied an extensive, brilliant description of a Peak district village, finding it amazing that they should turn from the moors towards the city while I am always looking from Manchester to the moors. But there is so much more about the moods and manners of a village here. I loved everything about it.
Completely by accident, we happened to visit this same village on Good Friday. The irony is that I had forgotten all about this while searching for a good walk, and in reading about the walk itself, had found only that Hadfield was one of the locations where League of Gentlemen was filmed. If you know it, you might recognise this view of Royston Vasey:
But what follows is a VERY long and wonderful description of Hadfield as was, under another pseudonym of Fetherhoughton.
At this early point, the topography of the village of Fetherhoughton may repay consideration. So may the manners, customs, and dress of its inhabitants. The village lay in moorland, which ringed it on three sides. The surrounding hills, from the village streets, looked like the hunched and bristling back of a sleeping dog. Let sleeping dogs lie, was the attitude of the people; for they hated nature. They turned their faces in the fourth direction, to the road and the railway that led them to the black heart of the industrial north: to Manchester, to Wigan, to Liverpool. They were not townspeople; they had none of their curiosity. They were not country people; they could tell a cow from a sheep, but it was not their business. Cotton was their business, and had been for nearly a century. There were three mills, but there were no clogs and shawls; there was nothing picturesque.
In summer the moorland looked black. Tiny distant figures swarmed over the hummocks and hills; they were Water Board men, Forestry Commission. In the folds of the hills there were pewtercoloured reservoirs, hidden from sight. The first event of autumn was the snowfall that blocked the pass that led through the moors to Yorkshire; this was generally accounted a good thing. All winter the snow lay on the hills. By April it had flaked off into scaly patches. Only in the warmest May would it seem to vanish entirely.
The people of Fetherhoughton kept their eyes averted from the moors with a singular effort of will. They did not talk about them. Someone –it was the mark of the outsider–might find a wild dignity and grandeur in the landscape. The Fetherhoughtonians did not look at the landscape at all. They were not Emily Bronte, nor were they paid to be, and the very suggestion that the Bronte-like matter was to hand was enough to make them close their minds and occupy their eyes with their shoelaces. The moors were the vast cemetery of their imaginations. Later, there were notorious murders in the vicinity, and real bodies were buried there.
The main street of Fetherhoughton was known to the inhabitants as Upstreet: "I am going Upstreet," they would say, "to the Co-op drapers." It was not unprosperous. Behind window displays of tinned salmon, grocers stood ready at their bacon slicers. Besides the Co-op draper, the Co-op general store, the Co-op butcher, the Co-op shoe shop, and the Co-op baker, there was Madame Hilda, Modes; and there was a hairdresser, who took the young women into private cubicles, segregated them with plastic curtains, and gave them Permanent Waves. There was no bookshop, nor anything of that sort. But there was a public library, and a war memorial.
Off Upstreet ran other winding streets with gradients of one in four, lined by terraced houses built in the local stone; they had been put up by the mill-owners towards the end of the last century, and rented out to the hands. Their front doors opened straight onto the pavement. There were two rooms downstairs, of which the sitting room was referred to as the House; so that in the unlikely event of anyone from Fetherhoughton explaining their conduct in any way, they might say, "I cleaned miyoopstairs this morning, this afternoon I am bound fert clean the House."
The speech of the Fetherhoughtonians is not easy to reproduce. The endeavour is false and futile. One misses the solemnity, the archaic formality of the Fetherhoughtonian dialect. It was a mode of speech, Father Angwin believed, that had come adrift from the language around it. Some current had caught them unawares, and washed the Fetherhoughtonians far from the navigable reaches of plain English; and there they drifted and bobbed on waters of their own, up the creek without a paddle.
But this is a digression, and in those houses there was no scope to digress. In the House there would be a coal fire, no heating in any other room, though there might be a single-bar electric fire kept, to be used in some ill-defined emergency. In the kitchen, a deep sink and a cold-water tap, and a very steep staircase, rising to the first floor. Two bedrooms, a garret: outside, a cobbled yard shared between some ten houses. A row of coalsheds, and a row of lavatories: to each house its own coalshed, but lavatories one between two. These were the usual domestic arrangements in Fetherhoughton and the surrounding districts.
Consider the women of Fetherhoughton, as a stranger might see them; a stranger might have the opportunity, because while the men were shut away in the mills the women liked to stand on their doorsteps. This standing was what they did. Recreational pursuits were for men: football, billiards, keeping hens. Treats were doled out to men, as a reward for good behaviour: cigarettes, beer at the Arundel Arms. Religion, and the public library, were for children. Women only talked. They analysed motive, discussed the serious business, carried life forward. Between the schoolroom and their present state came the weaving sheds; deafened by the noise of the machines, they spoke too loudly now, their voices scattering through the gritty streets like the cries of displaced gulls. Treeless streets, where the wind blows.
Consider their outdoor (not doorstep) dress. They wore plastic raincoats of a thick, viscous green, impermeable, like alien skins. Should it chance not to rain, the women rolled these raincoats up and left them about the house, where they appeared like reptiles from the Amazon, momentarily coiled in slumber.
For shoes, the women wore bedroom slippers in the form of bootees, with a big zip up the middle. When they went outdoors they put on a stouter version of the same shoe in a tough dark brown suede. Their legs rose like tubes, only an inch or so exposed beneath the hems of their big winter coats.
The younger women had different bedroom slippers, which relatives gave each other every Christmas. They were dish-shaped, each with a thick ruff of pink or blue nylon fur. At first the soles of these slippers were as hard and shiny as glass; it took a week of wear before they bent and gave under the foot, and during that week their wearer would often look down on them with pride, with a guilty sense of luxury, as the nylon fur tickled her ankles. But gradually the fur lost its bounce and spring, and crumbs fell into it; by February its fibres were matted together with chip fat.
From the doorsteps the women stared at passers-by, and laughed. They knew a joke, when it was pointed out to them, but for the most part their entertainment lay in the discernment of physical peculiarities in those around them. They lived in hope of seeing a passer-by with a hunchback, knock knees, or a hare lip. They did not think that it was cruel to mock the afflicted, they thought it was perfectly natural; they were sentimental but pitiless, very scathing, and unforgiving about any aberration, deviation, eccentricity, or piece of originality. There was a spirit abroad in the village that discriminated so thoroughly against pretension that it also discriminated against ambition, even against literacy.
Off Upstreet was Church Street, another steep hill; it was unpopulated, lined with ancient hedgerows, smoke and dust forming a perpetual ash-like deposit on the leaves. Church Street petered out at its summit into a wide track, muddy and stony, which in Fetherhoughton was known as the carriage-drive. Perhaps sometime in the last century a carriage had driven up it, conveying some pious person; the drive went nowhere except to the village school, to the convent, and to the Church of St. Thomas Aquinas. From the carriage-drive, footpaths led to the hamlet of Netherhoughton, and the moors.
Atop one of the smaller village streets sat a Methodist chapel, square and red, and about it was its cemetery, where chapel-going people came to early graves. There were a few Protestants sprinkled through the terraced rows; each yard might have some. The Protestants' houses did not have, pinned to the door of the cupboard in the sitting room, a coloured picture of the Pontiff with a calendar beneath; but otherwise, their houses were not readily distinguishable.
And yet the Protestants were quite different, in the eyes of their neighbours. They were guilty of culpable ignorance. They refused to take on board the precepts of the True Faith. They knew that St. Thomas Aquinas was there, but they refused to go in it. They refused to turn over their children to Mother Perpetua for a good Catholic education, and preferred to send them on a bus to a school in another village.
Mother Perpetua would tell the children, with her famous, dangerously sweet smile: "We have no objection to Protestants worshipping God in their own way. But we Catholics prefer to worship Him in his."
The Protestants were damned, of course, by reason of this culpable ignorance. They would roast in Hell. A span of seventy years, to ride bicycles in the steep streets, to get married, to eat bread and dripping; then bronchitis, pneumonia, a broken hip; then the minister calls, and the florist does a wreath; then devils will tear their flesh with pincers.
It is a most neighbourly thought. (11-13)
I found this quote too from Hilary Mantel in an interview with Jessica Jernigan.
HM: As I say in my author's note, Fetherhoughton is not to be found on a map, but there is a close geographical match in a village called Hadfield, in the Peak District of Derbyshire, where I was born in 1952. Hadfield has a twin village called Padfield, smaller still and nearer the moors. When I was 4 years old, the bishop of the diocese ordered the statues removed from the church, thus becoming a local hate figure. Earlier than this (my mother tells me) there had been a very popular young priest who disappeared overnight. So you might say I've amalgamated two parish legends. I remember that my mother was planning to offer a home to St. Gerard Majella, who stood six foot and was black all over, and is credited with offering special aid to women in childbirth. I heard adults talking, in the air above my head. One said "What are they going to do with the statues?" The other said "Bury them." A horrible shudder went through my infant frame. I know what I heard, but don't think they did bury them, and St. Gerard never did come to live with us. It's a mystery really.
We had gone to Hadfield for a walk, we were thinking about a longer walk up across the moors to Glossop but left late then still missed the train so ended up walking around the reservoirs, with a touch of the moors at least.
The reservoirs weren't quite beautiful for the most part, but rather full of fascination.
But we also escaped up, into the semi, sort-of wilds:
found a field of the tamest sheep I have ever encountered, all with their mouths open and tongues hanging out which is a funny look for sheep. Also, some damn cute lambs…
We passed a bronze age earthwork, bisected by a stone wall.
Found ruins and my favourite view of an aspirational sheep.
Another sheep with its flock of chickens, and an old trough
We skated in front of the rains
Not until we were almost back to the village did it suddenly occur to me where I knew the name Hadfield from, and that it was in fact the village of Fludd fame and where Hilary Mantel grew up. A matter of minutes later we found this sign about Brosscroft Road:
Strangely no mention of Fludd, but it did mean we could stop a moment in front of her old house and number 20:
walk down the street and have a pint in the New Lamp, stare briefly at the street where her aunt and uncle lived but the rain discouraged any exploration.
Still. A wonderful day. To end, my favourite quote of all from the book:
At midnight Fludd went out alone. It was cold, clear, still; a dried-up half-moon was skewered against the sky. The upper air was full of snow, the year's first. He could hear his own footsteps. He let his torch-beam loose among the trees, then brought it back to his side, as if it were a serpent he were training (129).
FetherhoughtonFluddHadfieldHilary MantelPeak DistrictRoyston Vaseywalking


컨트롤이나 해당 컨트롤의 자식 컨트롤이 현재 입력 포커스를 가지고 있으면 true이고, 그렇지 않으면 false입니다.true if the control or one of its child controls currently has the input focus; otherwise, false.
이 속성을 사용 하 여 컨트롤 또는 그 안에 포함 된 컨트롤에 입력된 포커스가 있는지 여부를 결정할 수 있습니다.You can use this property to determine whether a control or any of the controls contained within it has the input focus. 컨트롤에 포커스를 해당 자식 컨트롤의 모든 권한이 있는지 여부에 관계 없이 포커스가 있는지 여부를 확인 하려면 사용 된 Focused 속성입니다.To determine whether the control has focus, regardless of whether any of its child controls have focus, use the Focused property. 컨트롤에 입력된 포커스를 부여 하려면 사용 합니다 Focus 또는 Select 메서드.To give a control the input focus, use the Focus or Select methods.


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Leading tin producers to report on Code of Conduct standards
ITRI and member companies have developed a new industry Code of Conduct specifically designed for global tin mining and smelting operations and addressing the growing expectations of tin users and consumers. Now we are pleased to announce that our members, as leaders...
PT Timah renews commitment to tin industry body ITRI
Indonesian tin producer PT Timah has renewed its commitment to the global tin industry association ITRI as a key step forward in its mission to be a leading mining company in a world increasingly driven by sustainability issues. Representing the world's major tin...
ITRI wins edie Sustainable Supply Chains Leader 2017
ITRI's dedicated work and success in bringing positive change in the tin supply chain has been recognised with the award of the prestigious edie Sustainability Leaders Award 2017 for Sustainable Supply Chains. The winners were announced at an awards ceremony at the...


Filtered: Only entries tagged as Muppets displayed.
Pics of some of the amazing architecture on display at the Shanghai Expo.
More fun pieces from that Sidekicks and Henchmen art show.
Details and impressions on the "Mexican District 9," Monsters.
Syfy is considering doing another Battlestar Galactica spin-off show. Also, they've got two superhero-related shows in the works. One is called Three Inches, and it's a tongue-in-cheek, postmodern superhero story about a guy who can move things with his mind, but only three inches. He joins up with a bunch of folks with similarly questionable powers to make a super team. The other show is called Alphas, and also involves a super team, but that's about all that's known so far.
A few more details on that prequel of The Thing.
Looks like Jason Segel's Muppet movie is moving forward, and he'll be starring in it.
Chris Sims' ode to a particularly odd episode of G.I. Joe is a joy to read.
Supposedly the MacGruber movie is actually pretty good.
Not a review of Neil Marshall's Centurion, just a rundown of the kind of movie it is.