70 research outputs found
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
Asymptotic counting of BPS operators in superconformal field theories
We consider some aspects of counting BPS operators which are annihilated by
two supercharges, in superconformal field theories. For non-zero coupling, the
corresponding multi-variable partition functions can be written in terms of
generating functions for vector partitions or their weighted generalisations.
We derive asymptotics for the density of states for a wide class of such
multi-variable partition functions. We also point out a particular
factorisation property of the finite N partition functions. Finally, we discuss
the concept of a limit curve arising from the large N partition functions,
which is related to the notion of a typical state and discuss some implications
for the holographic duals.Comment: 39 pages latex. v2: minor improvements, reference adde
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
A Meinardus theorem with multiple singularities
Meinardus proved a general theorem about the asymptotics of the number of
weighted partitions, when the Dirichlet generating function for weights has a
single pole on the positive real axis. Continuing \cite{GSE}, we derive
asymptotics for the numbers of three basic types of decomposable combinatorial
structures (or, equivalently, ideal gas models in statistical mechanics) of
size , when their Dirichlet generating functions have multiple simple poles
on the positive real axis. Examples to which our theorem applies include ones
related to vector partitions and quantum field theory. Our asymptotic formula
for the number of weighted partitions disproves the belief accepted in the
physics literature that the main term in the asymptotics is determined by the
rightmost pole.Comment: 26 pages. This version incorporates the following two changes implied
by referee's remarks: (i) We made changes in the proof of Proposition 1; (ii)
We provided an explanation to the argument for the local limit theorem. The
paper is tentatively accepted by "Communications in Mathematical Physics"
journa
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
On the plane-wave cubic vertex
The exact bosonic Neumann matrices of the cubic vertex in plane-wave
light-cone string field theory are derived using the contour integration
techniques developed in our earlier paper. This simplifies the original
derivation of the vertex. In particular, the Neumann matrices are written in
terms of \mu-deformed Gamma-functions, thus casting them into a form that
elegantly generalizes the well-known flat-space solution. The asymptotics of
the \mu-deformed Gamma-functions allow one to determine the large-\mu behaviour
of the Neumann matrices including exponential corrections. We provide an
explicit expression for the first exponential correction and make a conjecture
for the subsequent exponential correction terms.Comment: 26 pages, 1 figure; harvmac (b); v4: minor corrections in appendix
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
Homogeneous Plane-wave Spacetimes and their Stability
We consider the stability of spatially homogeneous plane-wave spacetimes. We
carry out a full analysis for plane-wave spacetimes in (4+1) dimensions, and
find there are two cases to consider; what we call non-exceptional and
exceptional. In the non-exceptional case the plane waves are stable to
(spatially homogeneous) vacuum perturbations as well as a restricted set of
matter perturbations. In the exceptional case we always find an instability.
Also we consider the Milne universe in arbitrary dimensions and find it is also
stable provided the strong energy condition is satisfied. This implies that
there exists an open set of stable plane-wave solutions in arbitrary
dimensions.Comment: 15 pages, no figures; minor changes, new references, to appear in CQ
Minisuperspace Quantization of "Bubbling AdS" and Free Fermion Droplets
We quantize the space of 1/2 BPS configurations of Type IIB SUGRA found by
Lin, Lunin and Maldacena (hep-th/0409174), directly in supergravity. We use the
Crnkovic-Witten-Zuckerman covariant quantization method to write down the
expression for the symplectic structure on this entire space of solutions. We
find the symplectic form explicitly around AdS_5 x S^5 and obtain a U(1)
Kac-Moody algebra, in precise agreement with the quantization of a system of N
free fermions in a harmonic oscillator potential, as expected from AdS/CFT. As
a cross check, we also perform the quantization around AdS_5 x S^5 by another
method, using the known spectrum of physical perturbations around this
background and find precise agreement with our previous calculation.Comment: 22 Pages + 2 Appendices, JHEP3; v3: explanation of factor 2 mismatch
added, references reordered, published versio
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