All the solutions of the form M 2 × W Σ d − 2 for Lovelock gravity in vacuum in the Chern-Simons case
Open accessAbstract
In this paper we classify a certain family of solutions of Lovelock gravity in the Chern-Simons (CS) case, in arbitrary (odd) dimension, d ⩾ 5. The spacetime is characterized by admitting a metric that is a warped product of a two-dimensional spacetime M2 and an (a priori) arbitrary Euclidean manifold Σd−2 of dimension d − 2. We show that the solutions are naturally classified in terms of the equations that restrict Σd−2. According to the strength of such constraints we found the following branches in which Σd−2 has to fulfill: a Lovelock equation with a single vacuum (Euclidean Lovelock Chern-Simons in dimension d − 2), a single scalar equation that is the trace of an Euclidean Lovelock CS equation in dimension d − 2, or finally a degenerate case in which Σd−2 is not restricted at all. We show that all the cases have some degeneracy in the sense that the metric functions are not completely fixed by the field equations. This result extends the static five-dimensional case previously discussed in Dotti et al. [Phys. Rev. D 76, 064038 (2007)]10.1103/PhysRevD.76.064038, and it shows that in the CS case, the inclusion of higher powers in the curvature does not introduce new branches of solutions in Lovelock gravity. Finally, we comment on how the inclusion of a non-vanishing torsion may modify this analysis.
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These choices may even allow non-static solutions.
“These choices may even allow non-static solutions [11,14].”
From Birkhoff’s theorem in Lovelock gravity for general base manifolds (2015) · cites this paper as [14]
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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
- Oliva, J.
- Affiliations
- Austral University of Chile (CL)
- Corresponding author
- Oliva, Julio
- ORCID
- Oliva, Julio
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 2013-04-01
- Volume
- 54
- Issue
- 4
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W3103130442
- Cited by
- 19
- References
- 0
- Citations by year
- 2025: 2 · 2024: 1 · 2023: 2 · 2021: 1 · 2019: 1 · 2018: 1 · 2017: 1 · 2016: 1 · 2015: 2 · 2014: 4 · 2013: 3
- FWCI
- 1.37
- Type
- journal article
- Language
- en
- Open access
- green
- hdl.handle.net
- Licence
- other-oa
- Locations
- Journal of Mathematical Physics (publishedVersion)
- Repositorio Digital Institucional de la Universidad de Buenos Aires (Universidad de Buenos Aires) (publishedVersion, other-oa)
- LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) (publishedVersion, other-oa)
- arXiv (Cornell University) (submittedVersion)
- Americanae (AECID Library) (submittedVersion, other-oa)
- LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- Comisión Nacional de Investigación Científica y Tecnológica
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Keywords
- Lovelock gravity, Chern-Simons gravity, vacuum solutions, warped product metrics, higher-curvature gravity, odd-dimensional spacetime, static solutions, degenerate solutions, torsion, classification of solutions
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