Type II universal spacetimes

We study type II universal metrics of the Lorentzian signature. These metrics simultaneously solve vacuum field equations of all theories of gravitation with the Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its covariant derivatives of an arbi...

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Published inClassical and quantum gravity Vol. 32; no. 24; pp. 245012 - 245042
Main Authors Hervik, S, Málek, T, Pravda, V, Pravdová, A
Format Journal Article
LanguageEnglish
Published IOP Publishing 24.12.2015
Subjects
algebraically special spacetimes
Derivatives
Einstein spacetimes
generalized gravities
Gravitation
Gravitation theory
Invariants
Mathematical analysis
Polynomials
Prime numbers
Quantum gravity
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Summary:We study type II universal metrics of the Lorentzian signature. These metrics simultaneously solve vacuum field equations of all theories of gravitation with the Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its covariant derivatives of an arbitrary order. We provide examples of type II universal metrics for all composite number dimensions. On the other hand, we have no examples for prime number dimensions and we prove the non-existence of type II universal spacetimes in five dimensions. We also present type II vacuum solutions of selected classes of gravitational theories, such as Lovelock, quadratic and gravities.
Bibliography:CQG-101635.R1
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ISSN:0264-9381
1361-6382
DOI:10.1088/0264-9381/32/24/245012