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

The cosmological sector to the full non-linear topologically massive gravity (TMG) is obtained for localized sources of mass m and spin σ besides the asymptotically spinning conical flat sector previously obtained [A. Edery, M.B. Paranjape, gr-qc/9606029, to be published]. 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 μ→∞ unlike the flat sector.