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

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

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

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

Equilibrium configurations of fluids and their stability in higher dimensions

We study equilibrium shapes, stability and possible bifurcation diagrams of fluids in higher dimensions, held together by either surface tension or self-gravity. We consider the equilibrium shape and stability problem of self-gravitating spheroids, establishing the formalism to generalize the MacLaurin sequence to higher dimensions. We show that such simple models, of interest on their own, also provide accurate descriptions of their general relativistic relatives with event horizons. The examples worked out here hint at some model-independent dynamics, and thus at some universality: smooth objects seem always to be well described by both ``replicas'' (either self-gravity or surface tension). As an example, we exhibit an instability afflicting self-gravitating (Newtonian) fluid cylinders. This instability is the exact analogue, within Newtonian gravity, of the Gregory-Laflamme instability in general relativity. Another example considered is a self-gravitating Newtonian torus made of a homogeneous incompressible fluid. We recover the features of the black ring in general relativity.Comment: 42 pages, 11 Figures, RevTeX4. Accepted for publication in Classical and Quantum Gravity. v2: Minor corrections and references adde

Holographic Entanglement Entropy: An Overview

In this article, we review recent progresses on the holographic understandings of the entanglement entropy in the AdS/CFT correspondence. After reviewing the general idea of holographic entanglement entropy, we will explain its applications to confinement/deconfinement phase transitions, black hole entropy and covariant formulation of holography.Comment: 52 pages, Invited review article for a special issue "Entanglement entropy in extended quantum systems" in Journal of Physics A, edited by P.Calabrese, J. Cardy and B. Doyon; (v2) references adde