The general supersymmetric solution of topologically massive supergravity
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We find the general fully nonlinear 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 . If does not take the critical value, = 1, these solutions are asymptotically regular on a Poincar patch, but do not admit a smooth global compactification with boundary . In the critical case, the solutions have a logarithmic singularity on the boundary of the Poincar 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. 2008 IOP Publishing Ltd.