New vacuum solutions of conformal Weyl gravity

TL;DR

This paper completely solves the Bach equation for metrics conformally related to the product of two 2-spaces, providing new vacuum solutions in conformal Weyl gravity, including cosmological models.

Contribution

It introduces a covariant 2+2 decomposition approach to solve the Bach equation for specific conformal metrics, expanding the set of known vacuum solutions.

Findings

Explicit vacuum solutions for conformally related 2+2 metrics.

Application of 2-dimensional gravity results to Weyl gravity.

Presentation of new cosmological solutions.

Abstract

The Bach equation, i.e., the vacuum field equation following from the Lagrangian L=C_{ijkl}C^{ijkl}, will be completely solved for the case that the metric is conformally related to the cartesian product of two 2-spaces; this covers the spherically and the plane symmetric space-times as special subcases. Contrary to other approaches, we make a covariant 2+2-decomposition of the field equation, and so we are able to apply results from 2-dimensional gravity. Finally, some cosmological solutions will be presented and discussed.