Birkhoff’s theorem in Lovelock gravity
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We show that the solutions of the Lovelock equations with spherical, planar, or hyperbolic symmetry are locally isometric to the corresponding static Lovelock black hole. As a consequence, these solutions are locally static: they admit an additional Killing vector that can either be space-like or time-like, depending on the position. This result also holds in the presence of an abelian gauge field, in which case the solutions are locally isometric to a charged static black hole.
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Birkhoff's theorem also holds in Lovelock theory.
“Birkhoff's theorem also holds in Lovelock theory of gravity [4,5] which is a natural higher curvature generalization of Einstein's general relativity and retains the property that the field equations are of second order in the metric [6].”
From Birkhoff’s theorem in Lovelock gravity for general base manifolds (2015) · cites this paper as [4]
The theorem on p. 1 establishes a Birkhoff-type result for generic Lovelock field equations with spherical, planar, or hyperbolic symmetry. The qualification matters: the paper says fine-tuned Lovelock couplings can evade the theorem, so the unqualified claim is broader than its result. (LLM, conf=0.88)
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String-Generated Gravity Models
Boulware, D. G., & Deser, S. (1985) · Physical Review Letters · doi:10.1103/physrevlett.55.2656 · Cited by 1,583 · see citing works
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Research works printed but not linked: 5
- [1]N. Straumann, General Relativity , Springer-Verlag (2004)
- [4]R. G. Cai, Phys. Lett. B 582 , 237 (2004) [arXiv:hep-th/0311240]. · arXiv
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Generalized Misner-Sharp quasilocal mass in Einstein-Gauss-Bonnet gravity
Maeda, H., & Nozawa, M. (2008) · Physical Review D · doi:10.1103/physrevd.77.064031 · Cited by 155 · see citing works
Causality and hyperbolicity of Lovelock theories
Reall, H. S., Tanahashi, N., & Way, B. (2014) · Classical and Quantum Gravity · doi:10.1088/0264-9381/31/20/205005 · Cited by 92 · see citing works
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
- Zegers, R.
- Affiliations
- Université Paris-Sud (FR)
- Corresponding author
- Zegers, Robin
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 2005-07-01
- Volume
- 46
- Issue
- 7
- Pages
- 072502
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2054177163
- Cited by
- 104
- References
- 1
- Citations by year
- 2026: 3 · 2025: 4 · 2024: 6 · 2023: 1 · 2022: 2 · 2021: 1 · 2020: 3 · 2018: 4 · 2017: 3 · 2016: 6 · 2015: 4 · 2014: 7 · 2013: 7 · 2012: 13
- FWCI
- 2.56
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Mathematical Physics (publishedVersion)
- Durham Research Online (Durham University) (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Durham Research Online (Durham University) (submittedVersion, cc-by)
- 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 › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- Birkhoff's theorem, Lovelock gravity, static black holes, local isometry, Killing vector fields, spherical symmetry, planar symmetry, hyperbolic symmetry, Abelian gauge fields, charged black holes, higher-curvature gravity
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