Cosmological sector for localized mass and spin in 2+1 dimensional topologically massive gravity

TL;DR

This paper explores the cosmological sector of topologically massive gravity with localized mass and spin sources, revealing unique deficit angles and limitations in recovering Einstein gravity results.

Contribution

It derives the cosmological sector for localized sources in TMG, highlighting differences from Einstein gravity and the behavior of deficit angles.

Findings

Mass creates a negative deficit angle of 3m

Cannot recover Einstein gravity results as μ approaches infinity

Near sources, the metric resembles spinning conical flat metric

Abstract

The cosmological sector to the full non-linear topologically massive gravity (TMG) is obtained for localized sources of mass $m$ and spin $\sigma$ besides the asymptotically spinning conical flat sector previously obtained. In a small region near but outside the sources, the metric resembles the spinning conical flat metric, but we find that the mass $m$ creates a negative deficit angle of $3m$ as opposed to $m$. Furthermore, it is not possible to recover the results of pure Einstein gravity in the limit $\mu \to \infty$ unlike the flat sector.