# 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.

## Key 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.