Type II universal spacetimes

TL;DR

This paper investigates type II universal Lorentzian spacetimes that solve all polynomial curvature-based vacuum field equations across various gravitational theories, providing examples in composite dimensions and proving non-existence in five dimensions.

Contribution

It introduces the concept of type II universal metrics, offers examples in composite dimensions, and proves their non-existence in five dimensions, advancing understanding of universal spacetimes.

Findings

Examples of type II universal metrics in all composite dimensions.

Proof of non-existence of such metrics in five dimensions.

Type II vacuum solutions for specific gravitational theories.

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.