156 research outputs found
Electrovacuum Near-horizon Geometries in Four and Five Dimensions
Associated to every stationary extremal black hole is a unique near-horizon
geometry, itself a solution of the field equations. These latter spacetimes are
more tractable to analyze and most importantly, retain properties of the
original black hole which are intrinsic to the event horizon. After reviewing
general features of near-horizon geometries, such as SO(2,1) symmetry
enhancement, I report on recent work on stationary, charged extremal black hole
solutions of the Einstein-Maxwell equations with a negative cosmological
constant in four dimensions and present a classification of near-horizon
geometries of black holes on this kind. In five dimensions, charged extremal
black hole solutions to minimal (gauged) supergravity, which arises naturally
in string theory and the gauge theory/gravity correspondence, are considered. I
consider the classification of near-horizon geometries for the subset of such
black holes which are supersymmetric. Recent progress on the classification
problem in the general extremal, non-supersymmetric case is also discussed.Comment: Invited contribution to a special issue of Classical and Quantum
Gravity on the 19th International Conference on General Relativity and
Gravitation, Mexico City, July 5-9, 201
Uniqueness of near-horizon geometries of rotating extremal AdS(4) black holes
We consider stationary extremal black hole solutions of the Einstein-Maxwell
equations with a negative cosmological constant in four dimensions. We
determine all non-static axisymmetric near-horizon geometries (with
non-toroidal horizon topology) and all static near-horizon geometries for black
holes of this kind. This allows us to deduce that the most general near-horizon
geometry of an asymptotically globally AdS(4) rotating extremal black hole, is
the near-horizon limit of extremal Kerr-Newman-AdS(4). We also identify the
subset of near-horizon geometries which are supersymmetric. Finally, we show
which physical quantities of extremal black holes may be computed from the
near-horizon limit alone, and point out a simple formula for the entropy of the
known supersymmetric AdS(4) black hole. Analogous results are presented in the
case of vanishing cosmological constant.Comment: 18 pages, Latex. v2: footnote added on pg. 12. v3: assumption of
non-toroidal horizon topology made explicit, minor clarification
Constructing near-horizon geometries in supergravities with hidden symmetry
We consider the classification of near-horizon geometries in a general
two-derivative theory of gravity coupled to abelian gauge fields and uncharged
scalars in four and five dimensions, with one and two commuting rotational
symmetries respectively. Assuming that the theory of gravity reduces to a 3d
non-linear sigma model (as is typically the case for ungauged supergravities),
we show that the functional form of any such near-horizon geometry may be
determined. As an example we apply this to five dimensional minimal
supergravity. We also construct an example of a five parameter near-horizon
geometry solution to this theory with S^1 X S^2 horizon topology. We discuss
its relation to the near-horizon geometries of the yet to be constructed
extremal black rings with both electric and dipole charges.Comment: Latex, 30 pages. v2: discussion in section 5 modified and improved,
other minor changes, references adde
New thermodynamic identities for five-dimensional black holes
We derive new identities for the thermodynamic variables of five-dimensional,
asymptotically flat, stationary and biaxisymmetric vacuum black holes. These
identities depend on the topology of the solution and include contributions
arising from certain topological charges. The proof employs the harmonic map
formulation of the vacuum Einstein equations for solutions with these
symmetries.Comment: 5 pages. v2: minor edit
Near-horizon geometries of supersymmetric AdS(5) black holes
We provide a classification of near-horizon geometries of supersymmetric,
asymptotically anti-de Sitter, black holes of five-dimensional U(1)^3-gauged
supergravity which admit two rotational symmetries. We find three
possibilities: a topologically spherical horizon, an S^1 \times S^2 horizon and
a toroidal horizon. The near-horizon geometry of the topologically spherical
case turns out to be that of the most general known supersymmetric,
asymptotically anti-de Sitter, black hole of U(1)^3-gauged supergravity. The
other two cases have constant scalars and only exist in particular regions of
this moduli space -- in particular they do not exist within minimal gauged
supergravity. We also find a solution corresponding to the near-horizon
geometry of a three-charge supersymmetric black ring held in equilibrium by a
conical singularity; when lifted to type IIB supergravity this solution can be
made regular, resulting in a discrete family of warped AdS(3) geometries.
Analogous results are presented in U(1)^n gauged supergravity.Comment: Latex, 29 pages. v2: minor improvements, references adde
Central Charges in Extreme Black Hole/CFT Correspondence
The Kerr/CFT correspondence has been recently broadened to the general
extremal black holes under the assumption that the central charges from the
non-gravitational fields vanish. To confirm this proposal, we derive the
expression of the conserved charges in the Einstein-Maxwell-scalar theory with
topological terms in four and five dimensions and check that the above
assumption was correct. Combining the computed central charge with the expected
form of the temperature, the Bekenstein-Hawking entropy of the general extremal
black holes in four and five dimensions can be reproduced by using the Cardy
formula.Comment: 20 pages, v2:references added, published in JHE
CFT Duals for Extreme Black Holes
It is argued that the general four-dimensional extremal Kerr-Newman-AdS-dS
black hole is holographically dual to a (chiral half of a) two-dimensional CFT,
generalizing an argument given recently for the special case of extremal Kerr.
Specifically, the asymptotic symmetries of the near-horizon region of the
general extremal black hole are shown to be generated by a Virasoro algebra.
Semiclassical formulae are derived for the central charge and temperature of
the dual CFT as functions of the cosmological constant, Newton's constant and
the black hole charges and spin. We then show, assuming the Cardy formula, that
the microscopic entropy of the dual CFT precisely reproduces the macroscopic
Bekenstein-Hawking area law. This CFT description becomes singular in the
extreme Reissner-Nordstrom limit where the black hole has no spin. At this
point a second dual CFT description is proposed in which the global part of the
U(1) gauge symmetry is promoted to a Virasoro algebra. This second description
is also found to reproduce the area law. Various further generalizations
including higher dimensions are discussed.Comment: 18 pages; v2 minor change
Supersymmetric isolated horizons
We construct a covariant phase space for rotating weakly isolated horizons in
Einstein-Maxwell-Chern-Simons theory in all (odd) dimensions. In
particular, we show that horizons on the corresponding phase space satisfy the
zeroth and first laws of black-hole mechanics. We show that the existence of a
Killing spinor on an isolated horizon in four dimensions (when the Chern-Simons
term is dropped) and in five dimensions requires that the induced (normal)
connection on the horizon has to vanish, and this in turn implies that the
surface gravity and rotation one-form are zero. This means that the
gravitational component of the horizon angular momentum is zero, while the
electromagnetic component (which is attributed to the bulk radiation field) is
unconstrained. It follows that an isolated horizon is supersymmetric only if it
is extremal and nonrotating. A remarkable property of these horizons is that
the Killing spinor only has to exist on the horizon itself. It does not have to
exist off the horizon. In addition, we find that the limit when the surface
gravity of the horizon goes to zero provides a topological constraint.
Specifically, the integral of the scalar curvature of the cross sections of the
horizon has to be positive when the dominant energy condition is satisfied and
the cosmological constant is zero or positive, and in particular
rules out the torus topology for supersymmetric isolated horizons (unless
) if and only if the stress-energy tensor is of the form
such that for any two null vectors and with
normalization on the horizon.Comment: 26 pages, 1 figure; v2: typos corrected, topology arguments
corrected, discussion of black rings and dipole charge added, references
added, version to appear in Classical and Quantum Gravit
All Vacuum Near-Horizon Geometries in -dimensions with Commuting Rotational Symmetries
We explicitly construct all stationary, non-static, extremal near horizon
geometries in dimensions that satisfy the vacuum Einstein equations, and
that have commuting rotational symmetries. Our work generalizes
[arXiv:0806.2051] by Kunduri and Lucietti, where such a classification had been
given in . But our method is different from theirs and relies on a
matrix formulation of the Einstein equations. Unlike their method, this matrix
formulation works for any dimension. The metrics that we find come in three
families, with horizon topology , or ,
or quotients thereof. Our metrics depend on two discrete parameters specifying
the topology type, as well as continuous parameters. Not all of
our metrics in seem to arise as the near horizon limits of known
black hole solutions.Comment: 22 pages, Latex, no figures, title changed, references added,
discussion of the parameters specifying solutions corrected, amended to match
published versio
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