Uniqueness and Non-Uniqueness of Static Vacuum Black Holes in Higher Dimensions
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We prove the uniqueness theorem for asymptotically flat static vacuum black hole solutions in higher-dimensional space-times. We also construct infinitely many non-asymptotically flat regular static black holes on the same space-time manifold with the same spherical topology.
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Birkhoff's theorem in higher dimensions is valid for a wider class of metrics which include spacetimes with Böhm metrics existing on base manifolds topologically spheres or products thereof.
“Hence, Birkhoff's theorem in higher dimensions is valid for a wider class of metrics which in particular include spacetimes with the Böhm metrics existing on base manifolds which are topologically spheres or products thereoffoot_0 [1][2][3].”
From Birkhoff’s theorem in Lovelock gravity for general base manifolds (2015) · cites this paper as [2]
Section 3 (page unavailable) describes higher-dimensional, non-asymptotically flat static black-hole solutions obtained by using Böhm metrics in place of round sphere metrics. It does not establish the claimed extension of Birkhoff’s theorem or state that the Böhm metrics occur on products of spheres. (LLM, conf=0.84)
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Birkhoff’s theorem in Lovelock gravity for general base manifolds
Ray, S. (2015) · Classical and Quantum Gravity · doi:10.1088/0264-9381/32/19/195022 · Cited by 34 · see citing works
- Authors
- Gibbons, G. W., Ida, D., & Shiromizu, T.
- Affiliations
- University of Cambridge (GB)
- Tokyo Institute of Technology (JP)
- Venue
- Progress of Theoretical Physics Supplement
- Publisher
- Oxford University Press (OUP)
- Published
- 2002
- Volume
- 148
- Pages
- 284-290
- ISSN
- 0375-9687 (ISSN-L)
- OpenAlex
- W2963317489
- Cited by
- 164
- References
- 0
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 4 · 2023: 1 · 2022: 2 · 2021: 6 · 2020: 1 · 2019: 5 · 2018: 4 · 2017: 1 · 2015: 2 · 2014: 5 · 2013: 6 · 2012: 22
- FWCI
- 5.92
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Progress of Theoretical Physics Supplement (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Institutional Repositories DataBase (IRDB) (submittedVersion)
- HighWire Press Open Archive (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Keywords
- uniqueness theorem, static black holes, higher-dimensional spacetime, asymptotically flat spacetimes, regular black holes, non-uniqueness, spherical topology, static spacetimes
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