Type II universal spacetimes

Abstract

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 L(Riemann) gravities.

24 pages, matches published version in CQG

References in corpus (5)

• Algebraic classification of higher dimensional spacetimes based on null alignment
• Generalization of the Geroch-Held-Penrose formalism to higher dimensions
• Type D Einstein spacetimes in higher dimensions
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• From Smooth Curves to Universal Metrics
• Einstein-Maxwell fields with vanishing higher-order corrections
• $\mathcal{I}$-Preserving Diffeomorphisms of Lorentzian Manifolds
• Real GIT with applications to compatible representations and Wick-rotations
• Locally Homogeneous Kundt Triples and CSI Metrics
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