171 research outputs found
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
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
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
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
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
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
Finite N Index and Angular Momentum Bound from Gravity
We exactly compute the finite N index and BPS partition functions for N=4 SYM
theory in a newly proposed maximal angular momentum limit. The new limit is not
predicted from the superconformal algebra, but naturally arises from the
supergravity dual. We show that the index does not receive any finite N
corrections while the free BPS partition function does.Comment: 14 pages, v2: minor revisions, published versio
Near Horizon Analysis of Extremal AdS5 Black Holes
We study the near horizon geometry of extremal black holes in five
dimensional gauged supergravity using Sen's entropy function formalism. Special
attention is paid to the large black hole limit where the near horizon solution
exhibits a universal dependence on the rotation. The physical properties of the
large black hole solution are shown to agree with predictions from fluid
mechanical description of the dual conformal field theory.Comment: 26 pages, 1 figure; v2. clarifications and references adde
Near Extremal Kerr Entropy from AdS_2 Quantum Gravity
We analyze the asymptotic symmetries of near extremal Kerr black holes in
four dimensions using the AdS_2/CFT_1 correspondence. We find a Virasoro
algebra with central charge c_R=12J that is independent from the Virasoro
algebra (with the same central charge) that acts on the degenerate ground
state. The energy of the excitations is computed as well, and we can use
Cardy's formula to determine the near extremal entropy. Our result is
consistent with the Bekenstein-Hawking area law for near extremal Kerr black
holes.Comment: 28 pages. v2: references added, typos correcte
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