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

Abstract

Stationary solutions to the full non-linear topologically massive gravity (TMG) are obtained for localized sources of mass $m$ and spin $σ$. 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 $σ+ \frac{m}μ(\frac{4π+m}{4π+2m})$ depending on the structure of the spin source (here $μ$ 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 $σ$ contrary to a previous analysis by Clement.