Abstract
We briefly summarize our recent results on universal spacetimes. We show that universal spacetimes are necessarily CSI, i.e. for these spacetimes, all curvature invariants constructed from the Riemann tensor and its derivatives are constant. Then, we focus on type III universal spacetimes and discuss a proof of universality for a class of type III Kundt spacetimes. We also mention explicit examples of type III and II universal spacetimes.
Highlights
In the contribution [1] in this volume, we have introduced universal spacetimes obeying the following definition [2]Definition 1.1
A metric is called universal if all conserved symmetric rank-2 tensors constructed from the metric, the Riemann tensor and its covariant derivatives of arbitrary order are multiples of the metric
We have argued that universal metrics solve the vacuum equations of all theories of gravity with the Lagrangian of the form
Summary
In the contribution [1] in this volume, we have introduced universal spacetimes obeying the following definition [2]Definition 1.1. We expect that type III universal spacetimes are necessarily Kundt, in contrast to the type N case, we cannot use Theorem 1.2 to prove this statement in full generality and in [5], we provide a proof only in the “generic” case. We identify a universal subclass of type III Kundt metrics1
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