Black hole uniqueness theorems in higher dimensional spacetimes

2012/06/30 by Stefan Hollands, Akihiro Ishibashi · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Black hole (networking) #Geometric Analysis and Curvature Flows #Homogeneous space #Mathematical proof #Noncommutative and Quantum Gravity Theories #Topology (electrical circuits) #Uniqueness #Uniqueness theorem for Poisson's equation #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.1088/0264-9381/29/16/163001

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

openalex publication_date 2012/07/26 · arxiv created 2012/08/30 · arxiv updated 2015/06/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• Schwarzschild field inn dimensions and the dimensionality of space problem
• A classification of near-horizon geometries of extremal vacuum black holes
• The Geometry and Dynamics of Magnetic Monopoles
• On non-existence of static vacuum black holes with degenerate components of the event horizon
• Black strings andp-branes are unstable
• Black holes in general relativity
• On the proof of the positive mass conjecture in general relativity
• The Large Scale Structure of Space-Time
• The four laws of black hole mechanics
• 4-Dimensional black holes from Kaluza-Klein theories
• On the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon
• Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics
• A uniqueness theorem for five-dimensional Einstein–Maxwell black holes
• A new proof of the positive energy theorem
• Uniqueness of extremal Kerr and Kerr-Newman black holes
• Axisymmetric Black Hole Has Only Two Degrees of Freedom

Cited by

• Black holes with a single Killing vector field: black resonators

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