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.

A new supersymmetric, asymptotically anti-de Sitter, black hole solution of five-dimensional U (1) 3 gauged supergravity is presented. All known examples of such black holes arise as special cases of this solution, which is characterized by three charges and two angular momenta, with one constraint relating these five quantities. Analagous solutions of U (1) n gauged supergravity are also presented.

Any spacetime containing a degenerate Killing horizon, such as an extremal black hole, possesses a well-defined notion of a near-horizon geometry. We review such near-horizon geometry solutions in a variety of dimensions and theories in a unified manner. We discuss various general results including horizon topology and near-horizon symmetry enhancement. We also discuss the status of the classification of near-horizon geometries in theories ranging from vacuum gravity to Einstein-Maxwell theory and supergravity theories. Finally, we discuss applications to the classification of extremal black holes and various related topics. Several new results are presented and open problems are highlighted throughout.

Assessing the stability of higher-dimensional rotating black holes requires a study of linearized gravitational perturbations around such backgrounds. We study perturbations of Myers-Perry black holes with equal angular momenta in an odd number of dimensions (greater than five), allowing for a cosmological constant. We find a class of perturbations for which the equations of motion reduce to a single radial equation. In the asymptotically flat case we find no evidence of any instability. In the asymptotically anti-de Sitter case, we demonstrate the existence of a superradiant instability that sets in precisely when the angular velocity of the black hole exceeds the speed of light from the point of view of the conformal boundary. We suggest that the endpoint of the instability may be a stationary, nonaxisymmetric black hole.

We consider the near-horizon geometries of extremal, rotating black hole solutions of the vacuum Einstein equations, including a negative cosmological constant, in four and five dimensions. We assume the existence of one rotational symmetry in 4d, two commuting rotational symmetries in 5d and in both cases non-toroidal horizon topology. In 4d we determine the most general near-horizon geometry of such a black hole, and prove it is the same as the near-horizon limit of the extremal Kerr-AdS 4 black hole. In 5d, without a cosmological constant, we determine all possible near-horizon geometries of such black holes. We prove that the only possibilities are one family with a topologically S 1 × S 2 horizon and two distinct families with topologically S 3 horizons. The S 1 × S 2 family contains the near-horizon limit of the boosted extremal Kerr string and the extremal vacuum black ring. The first topologically spherical case is identical to the near-horizon limit of two different black hole solutions: the extremal Myers-Perry black hole and the slowly rotating extremal Kaluza-Klein (KK) black hole. The second topologically spherical case contains the near-horizon limit of the fast rotating extremal KK black hole. Finally, in 5d with a negative cosmological constant, we reduce the problem to solving a sixth-order non-linear ODE of one function. This allows us to recover the near-horizon limit of the known, topologically S 3 , extremal rotating AdS 5 black hole. Further, we construct an approximate solution corresponding to the near-horizon geometry of a small, extremal AdS 5 black ring.

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.This theory admits a 4-parameter non-supersymmetric black hole solution [3]. The 4 parameters are the 4 conserved charges of this theory, namely J 1 , J 2 , Q and the mass M . One might expect this to be the most general black hole of spherical topology. In the supersymmetric limit, one loses two parameters: supersymmetric black holes are parameterized by J 1 and J 2 . Returning to general (unequal) Q i , we would expect the most general nonsupersymmetric black hole to be parameterized by the 6 conserved charges J 1 , J 2 , Q 1 , Q 2 , Q 3 , M and losing 2 parameters in the supersymmetric limit would take one to the 4-parameter solution of [5]. There does not seem to be any room for an additional parameter.This objection rests on the assumption that black holes should be characterized by their conserved charges. Even in four dimensions, there is no uniqueness theorem for asymptotically AdS black holes, so maybe this assumption is incorrect even for topologically spherical AdS black holes. Furthermore, we know that this assumption is violated by black rings [9] in five asymptotically flat dimensions, which can require nonconserved charges to specify them fully [10]. It is natural to guess that the same is true in AdS. So perhaps the black holes of (ii) are supersymmetric AdS black rings. 1 The goal of this paper is to classify supersymmetric black holes in five-dimensional gauged supergravity. Unfortunately, finding rotating black hole solutions is hard, even with supersymmetry. We shall therefore adopt the approach initiated in [11] of classifying near-horizon geometries of supersymmetric black holes 2 . Obviously the existence of a near-horizon geometry with certain properties cannot be taken as a proof of the existence of a full black hole solution with those properties but this approach can be used to rule out certain types of solution. For example, if we find that near-horizon geometries with horizon topology S 1 × S 2 are not possible then that would exclude supersymmetric black rings.In minimal five-dimensional gauged supergravity, a classification of near-horizon geometries was attempted in [1]. However, the resulting equations proved too difficult to solve in full generality without additional assumptions. (This is in contrast with the ungauged theory, for which a full classi...

We present a new supersymmetric, asymptotically flat, black hole solution to five-dimensional supergravity. It is regular on and outside an event horizon of lens-space topology L(2,1). It is the first example of an asymptotically flat black hole with lens-space topology. The solution is characterized by a charge, two angular momenta, and a magnetic flux through a noncontractible disk region ending on the horizon, with one constraint relating these.

We propose a generalization of the (conformal) Killing-Yano equations relevant to D = 5 minimal gauged supergravity. The generalization stems from the fact that the dual of the Maxwell flux, the 3-form * F , couples naturally to particles in the background as a 'torsion'. Killing-Yano tensors in the presence of torsion preserve most of the properties of the standard Killing-Yano tensors-exploited recently for the higher-dimensional rotating black holes of vacuum gravity with cosmological constant. In particular, the generalized closed conformal Killing-Yano 2-form gives rise to the tower of generalized closed conformal Killing-Yano tensors of increasing rank which in turn generate the tower of Killing tensors. An example of a generalized Killing-Yano tensor is found for the Chong-Cvetić-Lü-Pope black hole spacetime [hepth/0506029]. Such a tensor stands behind the separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations in this background.