The General Supersymmetric Solution of Topologically Massive Supergravity

We find the general fully non-linear solution of topologically massive supergravity admitting a Killing spinor. It is of plane-wave type, with a null Killing vector field. Conversely, we show that all solutions with a null Killing vector are supersymmetric for one or the other choice of sign for the Chern-Simons coupling constant μ. If μdoes not take the critical value μ=\pm 1, these solutions are asymptotically regular on a Poincaré patch, but do not admit a smooth global compactification with boundary S^1\times\R. In the critical case, the solutions have a logarithmic singularity on the boundary of the Poincaré patch. We derive a Nester-Witten identity, which allows us to identify the associated charges, but we conclude that the presence of the Chern-Simons term prevents us from making a statement about their positivity. The Nester-Witten procedure is applied to the BTZ black hole.

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