Types III andNsolutions to quadratic gravity
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We study exact vacuum solutions to quadratic gravity (QG) of the Weyl types $N$ and III. We show that in an arbitrary dimension all Einstein spacetimes of the Weyl type $N$ with an appropriately chosen effective cosmological constant $\ensuremath{\Lambda}$ are exact solutions to QG and we refer to explicitly known metrics within this class. For type III Einstein spacetimes, an additional constraint follows from the field equations of QG and examples of spacetimes obeying such constraint are given. However, type III $pp$ waves do not satisfy this constraint and thus do not solve QG. For type $N$, we also study a wider class of spacetimes admitting a pure radiation term in the Ricci tensor. In contrast to the Einstein case, the field equations of generic QG determine optical properties of the geometry and restrict such exact solutions to the Kundt class. We provide examples of these metrics.
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Any Ricci flat type N spacetime is a solution of Lovelock theory with Λ = 0.
“We note that any such spacetime is a solution of Lovelock theory (with Λ = 0) (slightly extending a result of [13]).”
From Causality and hyperbolicity of Lovelock theories (2014) · cites this paper as [13]
Section II.A (p. 3) states that all Weyl type N Einstein spacetimes, which include Ricci-flat type N spacetimes, solve quadratic gravity with an appropriately chosen effective cosmological constant. Its footnote notes the Λ = 0 result for Gauss–Bonnet gravity. The paper does not establish the extension to Lovelock theory; the citing sentence itself calls that a slight extension of the cited result. (LLM, conf=0.86)
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Research works printed but not linked: 6
- [6]H. S. Reall. Algebraically special solutions in higher dimensions. arXiv:1105.4057 , 2011. · arXiv
- [8]D. Lovelock. Dimensionally dependent identities. Proc. Camb. Phil. Soc. , 68:345-350, 1970.
- [20]J. B. Griffiths and J. Podolsk´ y. Exact Space-Times in Einstein's General Relativity . Cambridge University Press, Cambridge, 2009.
- [24]H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, and E. Herlt. Exact Solutions of Einstein's Field Equations . Cambridge University Press, Cambridge, second edition, 2003.
- [28]A. A. Coley and S. Hervik. Universality and constant scalar curvature invariants. arXiv:1105.2356 2011. · arXiv
- [32]K. Peeters. Introducing Cadabra: A Symbolic computer algebra system for field theory problems. arXiv:hep-th/0701238 , 2007. · arXiv
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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
- Authors
- Málek, T., & Pravda, V.
- Affiliations
- Charles University (CZ)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2011-07-29
- Volume
- 84
- Issue
- 2
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2087061063
- Cited by
- 33
- References
- 0
- Citations by year
- 2025: 2 · 2024: 1 · 2023: 1 · 2022: 2 · 2021: 1 · 2020: 1 · 2019: 2 · 2018: 1 · 2017: 2 · 2016: 4 · 2015: 3 · 2014: 6 · 2013: 2 · 2012: 5
- FWCI
- 2.12
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- ASEP (submittedVersion, public-domain)
- arXiv (Cornell University)
- Funders
- Univerzita Karlova v Praze
- Grantová Agentura České Republiky
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Keywords
- quadratic gravity, exact vacuum solutions, Kundt spacetimes, pp-waves, effective cosmological constant, higher-dimensional gravity
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