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it is well known that in four space - time dimensions black holes satisfy the uniqueness theorem .
the theorem states that asymptotically flat non - degenerate black holes in einstein - maxwell theory are uniquely characterized by the global charges such as the mass , the angular momentum and the electric charge .
rotating black holes with electric charge are described by the kerr - newman solution , which is known in closed form .    in higher dimensions
this is no longer the case .
the schwarzschild , the reissner - nordstrm , and the kerr metric have closed - form generalizations .
but the rotating and electrically charged black hole in higher dimensional einstein - maxwell theory is not known analytically .
nevertheless , other analytical solutions have been obtained in more general theories .
one of these examples is found when a chern - simons term is added to the einstein - maxwell action in five dimensions @xcite . for a specific value of the chern - simons coupling ( supergravity ) , the general rotating and electrically charged black holes are known analytically .
a subset of these solutions are the bmpv black holes @xcite .
these black holes have vanishing angular velocity , but they are not static since the total angular momentum does not vanish .
in this paper we are interested in the generalization of these emcs black holes to general cs coupling constant .
since no general analytical solution is known , we will use numerical methods to generate the black holes and study their properties .
in addition to the numerical methods , we can obtain some properties of extremal emcs black holes if we study near - horizon solutions in the entropy function formalism @xcite .
in particular we will be interested in the solutions obtained when the cs coupling is greater than two times the supergravity value .
we will see that for these values of the cs coupling , an interesting new family of solutions is found @xcite .
let us start presenting the theory and ansatz .
einstein - maxwell - chern - simons theory in five dimensions has the following action :    @xmath0,\ ] ]    where @xmath1 is the curvature scalar and @xmath2 is the gauge potential with field strength tensor @xmath3 .
@xmath4 is the cs coupling parameter which in principle is free .
minimal 5-dimensional gauged supergravity is found for @xmath5 .
we choose the normalization so that @xmath6 . here
we are interested in asymptotically flat space - times . from this action
we obtain the field equations : @xmath7      we are interested in the 5-dimensional generalization of the kerr - newmann black holes , i.e. , stationary black holes with spherical horizon topology and axial symmetry .
hence the space - time has the killing vectors @xmath8 , @xmath9 and @xmath10 , where @xmath11 is a time - like coordinate , and @xmath12 , @xmath13 are two angular coordinates related to the two axes of rotation .
we restrict the black holes to have both angular momenta of equal magnitude , @xmath14 .
this means that the symmetry is enhanced to cohomogeneity-1 configurations .
all theses properties can be parametrized with the following ansatz for the metric @xmath15 where @xmath16 $ ] , @xmath17 $ ] and @xmath18 $ ] .
in addition , the ansatz for the gauge potential is @xmath19 the unknown metric and gauge potential functions depend only on the radial coordinate @xmath20 , which we will assume to be a quasi - isotropic radial coordinate .
the event horizon is located at @xmath21 , where @xmath22 . and
in particular extremal black holes are characterized by @xmath23 , @xmath24 .
black holes can be characterized by several properties like their global charges .
the existence of a time - like and angular killing vectors allows us to use the the komar formula to obtain the total mass @xmath25 and angular momentum @xmath26 of a configuration @xmath27 where @xmath28 and @xmath29 , @xmath30 .
we can also calculate the electric charge @xmath31 of the black hole , @xmath32 where @xmath33 .
the event horizon rotates with angular velocity @xmath34 , defined as @xmath35    other quantities of interest are related to the event horizon .
for example , the area of the event horizon @xmath36 and the horizon angular momentum @xmath37 are given by @xmath38 where @xmath39 represents the surface of the horizon .
we define the horizon angular momenta @xmath37 by the komar expression evaluated at the horizon .
note that equal - magnitude total angular momenta , @xmath40 , implies equal horizon angular momenta , @xmath41 .
also note that the area is related to the entropy : @xmath42 .
let us assume that the extremal black holes with event horizon of spherical topology have a near - horizon space - time with isometries given by @xmath44 .
an ansatz incorporating these symmetries @xcite is @xmath45 \\
\nonumber & + & v_2\eta[d\varphi_1+d\varphi_2+\cos{2\theta}(d\varphi_2-d\varphi_1)-\alpha \hat{r } dt]^2.\end{aligned}\ ] ] note that the horizon is at @xmath46 . for the gauge potential
we write @xmath47 the ansatz is described by the constant parameters @xmath48 , @xmath49 , @xmath50 , @xmath51 , @xmath52 and @xmath53 .
these parameters satisfy some constraints which can be obtained from the field equations , or equivalently from the near - horizon formalism .
the algebraic relations are @xmath54 and leave two undetermined parameters , which can be related to the angular momentum @xmath26 and the electric charge @xmath31 of the extremal black hole .
these two charges can be calculated using the associated noether charges @xcite .
the angular momentum @xmath26 is @xmath55 and the electric charge @xmath31 is @xmath56    we can calculate some horizon charges , such as the horizon angular momentum ( from the komar formula ) and horizon area : @xmath57
to obtain global solutions , we solve the emcs equations numerically .
we specify the usual boundary conditions for regular event horizon and asymptotic flatness .
we use a numerical package implementing a collocation method for boundary - value ordinary differential equations , with an adaptive mesh selection procedure @xcite .
let us present results for @xmath58 and fixed electric charge @xmath59 .
the properties obtained for these parameters are generic for other values of @xmath60 and @xmath43 .
the introduction of the cs term makes the theory no longer invariant under changes of sign of @xmath31 , for a fixed @xmath4 .
for instance consider @xmath61
. solutions . in figure
[ fig1 ] we can see that black holes with negative electric charge and @xmath43 have always a finite horizon area , and charged non - static solutions can be connected continuously with the charged static solution by continuously decreasing the angular momentum .
it can be demonstrated that the near - horizon solutions correspond one to one with the global solutions .
black holes with @xmath62 are completely different . a singular configuration with zero area is always found at some finite angular momentum .
this corresponds to the peaks around @xmath63 in figure [ fig1 ] .
black holes with a larger @xmath64 have finite horizon area , and again the near - horizon solutions correspond one to one with the global solutions . in figure [ fig1 ] it can be seen that for values of @xmath64 between the singular solutions , a complicated branch structure is found .
the structure contains cusps @xmath65}$ ] , where the mass reaches a local maximum , but also of the area .
the structure also contains branching points @xmath66},b^*_{[i , j]}$ ] , where two different solutions with the same global charges coexist .
the two solutions can be distinguished by their values of the horizon parameters ( area , horizon angular momentum ) .
this branch structure repeats an infinite number of times .
note that in the branch structure , we find non - static @xmath67 solutions , and we have labeled them with an integer number @xmath68 .
this number corresponds to the number of nodes of the functions @xmath69 and @xmath70 , and they can be understood as radially excited solutions .
the mass of these solutions increases discretely towards the mass of the static black hole .
surprisingly , the near - horizon solution of this family of solutions is always the same .      in figure [ fig2 ]
we present the domain of existence of the black holes we have considered , representing @xmath31 and @xmath26 scaled to the mass .
note that for positive @xmath31 , we have the branch structure of extremal solutions containing the radially excited black holes .
these extremal black holes do not form the boundary of the domain of existence .
in fact because of this , we can easily see in figure [ fig2 ] that there are non - extremal black holes with the same global quantities as these extremal solutions .
in particular , we show solutions with @xmath71 , intersecting in multiple points the extremal solutions .
hence , we can find two types of non - uniqueness .
in the previous section we have seen non - uniqueness between extremal solutions ( @xmath72 and @xmath73 ) , at the branching points of figure [ fig1 ] ) .
now we can see that there is also non - uniqueness between extremal and non - extremal solutions .
in addition we find that one near - horizon solution can correspond to only one global solution , multiple ( even infinite ) global solutions , or no global solution at all .
we gratefully acknowledge support by the dfg research training group 1620 `` models of gravity '' and by the spanish mineco , research project fis2011 - 28013 .
the work of e.r . is supported by the fct - if programme and the cidma strategic project uid / mat/04106/2013 .
we study the generalization of the kerr - newmann black hole in 5d einstein - maxwell - chern - simons theory with free chern - simons coupling parameter . 
 these black holes possess equal magnitude angular momenta and an event horizon of spherical topology . 
 we focus on the extremal case with zero temperature . 
 we find that , when the chern - simons coupling is greater than two times the supergravity case , new branches of black holes are found which violate uniqueness . 
 in particular , a sequence of these black holes are non - static radially excited solutions with vanishing angular momentum . 
 they approach the reissner - nordstrm solution as the excitation level increases .