Black hole uniqueness theorems and new thermodynamic identities in eleven dimensional supergravity

We consider stationary, non-extremal black holes in 11-dimensional supergravity having isometry group $\mathbb{R} \times U(1)^8$. We prove that such a black hole is uniquely specified by its angular momenta, its electric charges associated with the various 7-cycles in the manifold, together with certain moduli and vector valued winding numbers characterizing the topological nature of the spacetime and group action. We furthermore establish interesting, non-trivial, relations between the thermodynamic quantities associated with the black hole. These relations are shown to be a consequence of the hidden $E_{8(+8)}$ symmetry in this sector of the solution space, and are distinct from the usual "Smarr-type" formulas that can be derived from the first law of black hole mechanics. We also derive the "physical process" version of this first law applicable to a general stationary black hole spacetime without any symmetry assumptions other than stationarity, allowing in particular arbitrary horizon topologies. The work terms in the first law exhibit the topology of the horizon via the intersection numbers between cycles of various dimensions.Comment: 50pp, 3 figures, v2: references added, correction in appendix B, conclusions added, v3: reference section edited, typos removed, minor changes in appendix

Black hole instabilities and local Penrose inequalities

Various higher-dimensional black holes have been shown to be unstable by studying linearized gravitational perturbations. A simpler method for demonstrating instability is to find initial data that describes a small perturbation of the black hole and violates a Penrose inequality. An easy way to construct initial data is by conformal rescaling of the unperturbed black hole initial data. For a compactified black string, we construct initial data which violates the inequality almost exactly where the Gregory-Laflamme instability appears. We then use the method to confirm the existence of the "ultraspinning" instability of Myers-Perry black holes. Finally we study black rings. We show that "fat" black rings are unstable. We find no evidence of any rotationally symmetric instability of "thin" black rings.Comment: 35 pages, 12 figures. v2: typos corrected, matches published versio

Black hole uniqueness theorems in higher dimensional spacetimes

We review uniqueness theorems as well as other general results about higher dimensional black hole spacetimes. This includes in particular theorems about the topology of higher dimensional spacetimes, theorems about their symmetries (rigidity theorem), and the classification of supersymmetric black holes. We outline the basic ideas underlying the proofs of these statements, and we also indicate ways to generalize some of these results to more general contexts, such as more complicated theories.Comment: Extended version of "Topical Review" article commissioned by Class. Quant. Grav., 66 pages, several figures, Latex. v2: Added section on near horizon geometries, edited/added reference