Almost universal spacetimes in higher-order gravity theories

TL;DR

This paper introduces the concept of almost universal spacetimes in higher-order gravity theories, proving their properties and providing explicit examples, which simplifies the field equations and aids in finding new solutions.

Contribution

It defines and characterizes almost universal spacetimes, proves their properties in various dimensions, and provides explicit examples and new solutions in quadratic and conformal gravity.

Findings

All d-dimensional Kundt spacetimes of Weyl type III and traceless Ricci type N are almost universal.

Explicit examples of Weyl type II almost universal Kundt metrics are constructed.

Simplification of field equations enables discovery of new vacuum solutions in higher-order gravity theories.

Abstract

We study almost universal spacetimes - spacetimes for which the field equations of any generalized gravity with the Lagrangian constructed from the metric, the Riemann tensor and its covariant derivatives of arbitrary order reduce to one single differential equation and one algebraic condition for the Ricci scalar. We prove that all d-dimensional Kundt spacetimes of Weyl type III and traceless Ricci type N are almost universal. Explicit examples of Weyl type II almost universal Kundt metrics are also given. The considerable simplification of the field equations of higher-order gravity theories for almost universal spacetimes is then employed to study new Weyl type II, III, and N vacuum solutions to quadratic gravity in arbitrary dimension and six-dimensional conformal gravity. Necessary conditions for almost universal metrics are also studied.