A theorem on topologically massive gravity

TL;DR

This paper proves that in three-dimensional topologically massive gravity, only flat spacetime solutions exist without spin, highlighting the necessity of spin to support topological mass.

Contribution

It demonstrates that hypersurface orthogonal Killing vector fields restrict solutions to flat spacetime, showing spin is essential for non-trivial topologically massive gravity solutions.

Findings

Only trivial flat spacetime solutions exist without spin.

Spin is necessary to support topological mass in 3D gravity.

Hypersurface orthogonal Killing vectors constrain solutions.

Abstract

We show that for three dimensional space-times admitting a hypersurface orthogonal Killing vector field Deser, Jackiw and Templeton's vacuum field equations of topologically massive gravity allow only the trivial flat space-time solution. Thus spin is necessary to support topological mass.