Exact Solutions in Weyl-Cubed Gravity

TL;DR

This paper explores exact classical solutions in Weyl-cubed gravity, a higher-curvature gravitational theory, revealing various background geometries including conformally flat, Lifshitz, Schr"{o}dinger, and hyperscaling-violating solutions.

Contribution

It provides the first comprehensive analysis of exact solutions in Weyl-cubed gravity, including pure, Einstein plus Weyl-cubed, and matter-coupled cases.

Findings

Existence of conformally flat solutions

Lifshitz and Schr"{o}dinger backgrounds found

Hyperscaling-violating solutions identified

Abstract

A unitary gravitational action up to third order of curvature in which respects to the holographic $a-$theorem has been constructed in \cite{myers}. In particular, its third order term is just the Weyl-cubed term in four dimensions. In this paper, we study this theory and find some its exact classical solutions. We show that the theory admits conformally flat, Lifshitz, Schr\"{o}dinger and also hyperscaling-violating backgrounds as the solutions of equations of motion. Our analysis has been done for the pure Weyl-cubed gravity, Einstein plus Weyl-cubed term and gravity with matter.