Abstract
Universal spacetimes are exact solutions to all higher-order theories of gravity. We study these spacetimes in four dimensions and provide necessary and sufficient conditions for universality for all Petrov types except of type II. We show that all universal spacetimes in four dimensions are algebraically special and Kundt. Petrov type D universal spacetimes are necessarily direct products of two 2-spaces of constant and equal curvature. Furthermore, type II universal spacetimes necessarily possess a null recurrent direction and they admit the above type D direct product metrics as a limit. Such spacetimes represent gravitational waves propagating on these backgrounds. Type III universal spacetimes are also investigated. We determine necessary and sufficient conditions for universality and present an explicit example of a type III universal Kundt non-recurrent metric.
Highlights
Note that CSI is a necessary but not a sufficient condition for universality
Universal spacetimes are exact solutions to all higher-order theories of gravity. We study these spacetimes in four dimensions and provide necessary and sufficient conditions for universality for all Petrov types except of type II
For type N, we have found necessary and sufficient conditions for universality [10]: Proposition 1.3
Summary
By proposition 1.2, we can restrict ourselves to CSI spacetimes It has been shown in [17] that CSI spacetimes in four dimensions are either (locally) homogeneous or CSI degenerate Kundt metrics.. It remains to study type I locally homogeneous spacetimes. For type I universal spacetimes, we have to restrict ourselves to the Ricci-flat case. Theorem 12.1 of [15] states that all non-flat Ricci-flat homogeneous solutions with a multiply transitive group are certain plane waves (of type N). This metric is the only type I CSI Einstein metric and the only type I candidate for a universal metric.
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