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 $\sigma$. 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.

revised version, minor corrections, latex, 8 pages

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