Circular Symmetry in Topologically Massive Gravity

TL;DR

This paper presents a simplified derivation of a decoupling theorem in topologically massive gravity (TMG) for circularly symmetric spaces, and extends it to include null matter sources, clarifying the structure of solutions.

Contribution

It provides a compact re-derivation of the TMG decoupling theorem and generalizes it to matter fields, specifically null matter, in circular symmetry.

Findings

TMG separates into Einstein and Cotton sectors under circular symmetry.

The decoupling theorem is extended to include null matter sources.

The approach simplifies understanding of TMG solutions with symmetry and matter.

Abstract

We re-derive, compactly, a TMG decoupling theorem: source-free TMG separates into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal Killing vector, here concretely for circular symmetry. We can then generalize it to include matter, which is necessarily null.