pp Waves of Conformal Gravity with Self-Interacting Source

TL;DR

This paper explores pp wave solutions in a conformal gravity model with a self-interacting scalar source, revealing its equivalence to topologically massive gravity with a cosmological constant.

Contribution

It introduces a self-interacting potential into conformal gravity with scalar sources and demonstrates the equivalence to topologically massive gravity.

Findings

PP wave solutions exist in the self-interacting conformal gravity model.

The model is equivalent to topologically massive gravity with a specific cosmological constant.

The potential strength determines the cosmological constant value.

Abstract

Recently, Deser, Jackiw and Pi have shown that three-dimensional conformal gravity with a source given by a conformally coupled scalar field admits pp wave solutions. In this letter, we consider this model with a self-interacting potential preserving the conformal structure. A pp wave geometry is also supported by this system and, we show that this model is equivalent to topologically massive gravity with a cosmological constant whose value is given in terms of the potential strength.