Localized mass and spin in 2 + 1 dimensional topologically massive gravity

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 + mμ(4π + m4π + 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 [2].