Homogeneous anisotropic solutions of topologically massive gravity with cosmological constant and their homogeneous deformations

TL;DR

This paper classifies homogeneous anisotropic solutions in topologically massive gravity with a cosmological constant, explores their deformations, and clarifies properties of specific spacetimes like de Sitter and warped de Sitter.

Contribution

It provides a systematic analysis of homogeneous anisotropic solutions in TMG and examines their deformations, extending understanding of solution space in this theory.

Findings

Reproduces known homogeneous solutions in TMG.

Shows de Sitter and hyperbolic spaces cannot be infinitesimally deformed homogeneously.

Discusses properties of warped de Sitter spacetime.

Abstract

We solve the equations of topologically massive gravity with potentially non-vanishing cosmological constant for homogeneous metrics without isotropy. We only reproduce known solutions. We also discuss their homogeneous deformations, possibly with isotropy. We show that de Sitter space and hyperbolic space cannot be infinitesimally homogeneously deformed in TMG. We clarify some of their Segre-Petrov types and discuss the warped de Sitter spacetime.