Uniqueness and Nonuniqueness of Static Black Holes in Higher Dimensions
Open accessAbstract
We prove a uniqueness theorem for asymptotically flat static charged dilaton black-hole solutions in higher-dimensional space-times. We also construct infinitely many nonasymptotically flat regular static black holes on the same space-time manifold with the same spherical topology. An application to the uniqueness of a class of flat p-branes is also given.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
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 [3]
The concluding discussion (p. 4, around Eq. 40) says that replacing a round-sphere metric with Böhm Einstein metrics yields non-asymptotically flat static black-hole solutions. It does not establish Birkhoff’s theorem for that wider class; it expressly leaves the uniqueness of black holes constructed from the same Böhm metric open. (LLM, conf=0.86)
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cited by
Sorted by citations
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)
- Research Center for the Early Universe (JP)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2002-07-09
- Volume
- 89
- Issue
- 4
- Pages
- 041101-041101
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W3007627468
- Cited by
- 193
- References
- 0
- Citations by year
- 2026: 4 · 2025: 6 · 2024: 4 · 2023: 3 · 2022: 3 · 2021: 4 · 2020: 4 · 2019: 3 · 2018: 4 · 2017: 1 · 2016: 3 · 2015: 3 · 2014: 8 · 2013: 10 · 2012: 18
- FWCI
- 7.36
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Institutional Repositories DataBase (IRDB) (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
- static black holes, uniqueness theorem, non-uniqueness, higher-dimensional black holes, charged dilaton black holes, asymptotically flat spacetimes, spherical topology
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
