The Birkhoff theorem for topologically massive gravity

TL;DR

This paper derives the general class of solutions for topologically massive gravity in vacuum and with a cosmological constant, revealing conditions for Ricci-flatness and effects of spin on solutions.

Contribution

It provides the first comprehensive derivation of the $ ext{Sigma}_2 imes S$ solutions in topologically massive gravity, including cases with non-zero spin.

Findings

Derived the general $ ext{Sigma}_2 imes S$ solutions in vacuum and with cosmological constant.

Showed solutions have constant Ricci tensor and reduce to three-dimensional Einstein equations.

Discussed emergence of non-Ricci flat solutions when spin is introduced.

Abstract

We derive the general $\Sigma_2\times S$ solution of topologically massive gravity in vacuum and in presence of a cosmological constant. The field equations reduce to three-dimensional Einstein equations and the solution has constant Ricci tensor. We briefly discuss the emergence of non-Ricci flat solutions when spin is introduced.