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.
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Numerical simulations in 4+1 dimensions show near-extremal Schwarzschild-de Sitter black holes forming from gravitational wave collapse with mass over 99% of the extremal limit, suggesting the third law may not apply in cosmological settings.
Proves that a class of quasi-Einstein structures on closed manifolds admit a Killing vector field, extending prior rigidity results and completing classification for compact 2-manifolds while providing new examples.
Constructs all axi-symmetric non-gradient m-quasi-Einstein structures on S^2, including new hypergeometric metrics for m≠2 and a uniqueness theorem showing only the flat torus for m=-1 with zero cosmological constant.
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