All supersymmetric degenerate Killing horizons with closed spatial cross sections in D=11 supergravity are either isometric to near-horizon geometries or have vanishing spinorial Lie derivative and are pp-waves when possessing more than 13 supersymmetries.
The Geometry of D=11 Null Killing Spinors
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abstract
We determine the necessary and sufficient conditions on the metric and the four-form for the most general bosonic supersymmetric configurations of D=11 supergravity which admit a null Killing spinor i.e. a Killing spinor which can be used to construct a null Killing vector. This class covers all supersymmetric time-dependent configurations and completes the classification of the most general supersymmetric configurations initiated in hep-th/0212008.
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Classification of Killing Horizons in D=11 Supergravity
All supersymmetric degenerate Killing horizons with closed spatial cross sections in D=11 supergravity are either isometric to near-horizon geometries or have vanishing spinorial Lie derivative and are pp-waves when possessing more than 13 supersymmetries.