Abstract
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 μ. If μ does not take the critical value, μ = ±1, these solutions are asymptotically regular on a Poincaré 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 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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