Black hole uniqueness theorems in higher dimensional spacetimes

Abstract

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.

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 references

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Cited by in corpus (43)

• Classification of near-horizon geometries of extremal black holes
• Black holes, hidden symmetries, and complete integrability
• Love symmetry
• No Inner-Horizon Theorem for Black Holes with Charged Scalar Hairs
• Black holes with a single Killing vector field: black resonators
• Massive Scalar Perturbations on Myers-Perry-de Sitter Black Holes with a Single Rotation
• Black hole non-uniqueness via spacetime topology in five dimensions
• Uniqueness of photon sphere for Einstein-Maxwell-dilaton black holes with arbitrary coupling constant
• Charged black holes in Einsteinian cubic gravity and nonuniqueness
• Charged Black Rings at large D
• Black Holes with MDRs and Bekenstein-Hawking and Perelman Entropies for Finsler-Lagrange-Hamilton Spaces
• Moduli space of supersymmetric solitons and black holes in five dimensions
• Real ADE-equivariant (co)homotopy and Super M-branes
• Static and radiating p-form black holes in the higher dimensional Robinson-Trautman class
• Static spacetimes with/without black holes in dynamical Chern-Simons gravity
• Virasoro hair and entropy for axisymmetric Killing horizons
• New Restrictions on the Topology of Extreme Black Holes
• Uniqueness of charged static asymptotically flat black holes in dynamical Chern-Simons gravity
• Abelian-Higgs hair on stationary axisymmetric black hole in Einstein-Maxwell-axion-dilaton gravity
• Supersymmetric black hole non-uniqueness in five dimensions
• On the uniqueness of supersymmetric AdS${}_5$ black holes with toric symmetry
• Uniqueness of the extremal Schwarzschild de Sitter spacetime
• Supersymmetric black holes with a single axial symmetry in five dimensions
• On the nonexistence of a vacuum black lens
• Strictly static spacetimes and positive mass in the Einstein-Gauss-Bonnet theory
• Generalizations and challenges for the spacetime block-diagonalization
• Soliton mechanics
• Uniqueness of dilaton Melvin-Schwarzschild solution
• 5-Dimensional Space-Periodic Solutions of the Static Vacuum Einstein Equations
• Gravitational Chern-Simons terms and black hole entropy. Global aspects
• Multipole Hair of Schwarzschild-Tangherlini Black Holes
• Static black holes and strictly static spacetimes in Einstein-Gauss-Bonnet gravity with gauge field
• Stable circular orbits in caged black hole spacetimes
• Uniqueness of dark matter magnetized static black hole spacetime
• The Angular Tension of Black Holes
• Bounding Horizon Area by Angular Momentum, Charge, and Cosmological Constant in 5-Dimensional Minimal Supergravity
• A Bakry-Émery Almost Splitting Result With Applications to the Topology of Black Holes
• A classification of supersymmetric Kaluza-Klein black holes with a single axial symmetry
• Existence and Uniqueness of Near-Horizon Geometries for 5-Dimensional Black Holes
• Kerr-AdS type higher dimensional black holes with non-spherical cross-sections of horizons
• The electric field of a charge in the vicinity of a higher dimensional black hole
• Extrinsic black hole uniqueness in pure Lovelock gravity
• Electric Multipole Fields of Higher-Dimensional Massive Bodies