Cotton Blend Gravity $pp$ Waves

TL;DR

This paper investigates conformal gravity in 2+1 dimensions with a focus on $pp$ wave solutions, establishing an exact solution and demonstrating its equivalence to topologically massive gravity, thus linking different gravitational models.

Contribution

It provides the first exact $pp$ wave solutions in conformal gravity and shows their equivalence to topologically massive gravity in three dimensions.

Findings

Exact $pp$ wave solutions in conformal gravity

Equivalence between conformal gravity and topologically massive gravity

Insight into matter coupling in 2+1 gravity theories

Abstract

We study conformal gravity in d=2+1, where the Cotton tensor is equated to a--necessarily traceless--matter stress tensor, for us that of the improved scalar field. We first solve this system exactly in the $pp$ wave regime, then show it to be equivalent to topologically massive gravity.