Abstract
Using an off-shell Killing spinor analysis we perform a systematic investigation of the supersymmetric background and black hole solutions of the \( \mathcal{N}=\left(1,\;1\right) \) Cosmological New Massive Gravity model. The solutions with a null Killing vector are the same pp-wave solutions that one finds in the \( \mathcal{N}=1 \) model but we find new solutions with a time-like Killing vector that are absent in the \( \mathcal{N}=1 \) case. An example of such a solution is a Lifshitz spacetime. We also consider the supersymmetry properties of the so-called rotating hairy BTZ black holes and logarithmic black holes in an AdS 3 background. Furthermore, we show that under certain assumptions there is no supersymmetric Lifshitz black hole solution.
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Alkaç, G., Basanisi, L., Bergshoeff, E.A. et al. Supersymmetric backgrounds and black holes in \( \mathcal{N}=\left(1,\;1\right) \) cosmological new massive supergravity. J. High Energ. Phys. 2015, 141 (2015). https://doi.org/10.1007/JHEP10(2015)141
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DOI: https://doi.org/10.1007/JHEP10(2015)141