25 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
Two remarks on near-horizon geometries
We show that any extreme black hole with an orthogonally transitive abelian
isometry group has a near-horizon geometry with enhanced symmetry. We also
point out a simple proof of the horizon topology theorem of Galloway and Schoen
for degenerate horizons.Comment: 5 page
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
Do supersymmetric anti-de Sitter black rings exist?
We determine the most general near-horizon geometry of a supersymmetric,
asymptotically anti-de Sitter, black hole solution of five-dimensional minimal
gauged supergravity that admits two rotational symmetries. The near-horizon
geometry is that of the supersymmetric, topologically spherical, black hole
solution of Chong et al. This proves that regular supersymmetric anti-de Sitter
black rings with two rotational symmetries do not exist in minimal
supergravity. However, we do find a solution corresponding to the near-horizon
geometry of a supersymmetric black ring held in equilibrium by a conical
singularity, which suggests that nonsupersymmetric anti-de Sitter black rings
may exist but cannot be "balanced" in the supersymmetric limit.Comment: Latex, 18 pages, 1 figure. v2: minor change
No static bubbling spacetimes in higher dimensional Einstein-Maxwell theory
We prove that any asymptotically flat static spacetime in higher dimensional
Einstein-Maxwell theory must have no magnetic field. This implies that there
are no static soliton spacetimes and completes the classification of static
non-extremal black holes in this theory. In particular, these results establish
that there are no asymptotically flat static spacetimes with non-trivial
topology, with or without a black hole, in Einstein-Maxwell theory.Comment: 9 pages. v2: minor edits, references adde
Near-horizon symmetries of extremal black holes
Recent work has demonstrated an attractor mechanism for extremal rotating
black holes subject to the assumption of a near-horizon SO(2,1) symmetry. We
prove the existence of this symmetry for any extremal black hole with the same
number of rotational symmetries as known four and five dimensional solutions
(including black rings). The result is valid for a general two-derivative
theory of gravity coupled to abelian vectors and uncharged scalars, allowing
for a non-trivial scalar potential. We prove that it remains valid in the
presence of higher-derivative corrections. We show that SO(2,1)-symmetric
near-horizon solutions can be analytically continued to give SU(2)-symmetric
black hole solutions. For example, the near-horizon limit of an extremal 5D
Myers-Perry black hole is related by analytic continuation to a non-extremal
cohomogeneity-1 Myers-Perry solution.Comment: 21 pages, latex. v2: minor improvements v3: Corrected error in
argument excluding de Sitter and Poincare-symmetric cases. Results unaffecte
On Uniqueness of supersymmetric Black holes in AdS(5)
We study the possibility of having Black hole of spherical and ring horizon
topology with five independent charges in the -model of 5D gauge
supergravity. To study these possibilities we consider not only the known
result obtained by local supersymmetry analysis but include the input coming
from non-local properties of the solutions, like the attractor mechanism, the
entropy function of Sen, the Euclidean formulation and general properties of
the uplift to ten dimension. For the spherical case, we found that there is no
room for more general Black holes than the ones already describe in
hep-th/0601156. On the other hand, if a solution of ring horizon topology
exists, we conclude that it must be labeled by three independent parameters
only, since it has to satisfy two independent constraints that we explicitly
find in terms of its chemical potentials. At the end of the article, based on
all the local and non-local information, we put forward a conjecture on the
constraints that characterize general Black holes dual to SYM.Comment: 16 pages, typos corrected and references adde
On the uniqueness of extremal vacuum black holes
On the uniqueness of extremal vacuum blac