Localized Mass and Spin Sources in 2+1 Dimensional Topologically Massive Gravity

TL;DR

This paper derives stationary solutions in 2+1 dimensional topologically massive gravity with localized mass and spin sources, revealing how the topological term influences spin and clarifying constraints on point-like sources.

Contribution

It provides explicit solutions for localized mass and spin in TMG and analyzes the effects of the topological term on total spin, challenging previous assumptions about point-like sources.

Findings

Topological term induces spin in solutions.

Total spin varies depending on source structure.

Point-like sources face inconsistencies with delta functions.

Abstract

Stationary solutions to the full non-linear topologically massive gravity (TMG) are obtained for localized sources of mass $m$ and spin $\sigma$. Our results show that the topological term induces spin and that the total spin J (which is the spin observed by an asymptotic observer) ranges from 0 to $\sigma + \frac{m}{\mu}(\frac{4\pi+m}{4\pi +2m})$ depending on the structure of the spin source (here $\mu$ is the topological mass). We find that it is inconsistent to consider actual delta function mass and spin sources. In the point-like limit, however, we find no condition constraining $m$ and $\sigma$ contrary to a previous analysis by Clement.