Classification of solutions in topologically massive gravity

TL;DR

This paper classifies solutions in topologically massive gravity, revealing that algebraic type D solutions are biaxially squashed AdS_3 and reviewing known solutions' local equivalences.

Contribution

It provides a comprehensive algebraic classification of solutions in topologically massive gravity, identifying the nature of type D solutions and reviewing existing solutions.

Findings

Type D solutions are biaxially squashed AdS_3.

Most known solutions are locally equivalent to biaxially squashed AdS_3 or AdS pp-waves.

The paper offers a complete review of literature on solutions in this theory.

Abstract

We study exact solutions of three-dimensional gravity with a cosmological constant and a gravitational Chern-Simons term: the theory known as topologically massive gravity. After reviewing the algebraic classification, we show that if a solution has curvature of algebraic type D, then it is biaxially squashed AdS_3. Applying the classification, we provide a comprehensive review of the literature, showing that most known solutions are locally equivalent to biaxially squashed AdS_3 or to AdS pp-waves.