Universal spacetimes

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Written by Tomáš Málek

Universal metrics solve, by definition, vacuum equations of all theories of gravitation with the Lagrangian described by any polynomial curvature invariant constructed from the metric, the Riemann tensor and its covariant derivatives of arbitrary order. Thus, all quantum corrections vanish for these metrics. We will study Weyl type II, III and N universal spacetimes of Lorentzian signature in arbitrary dimension and provide examples of such metrics. We will also discuss metrics of neutral signature. It turns out, in contrast to the Lorentzian case, that universal metrics of neutral signature need not to belong to the Kundt class.