Oliver Lindblad Petersen (Stanford)
Moncrief and Isenberg conjectured in 1983 that any compact Cauchy horizon in a smooth vacuum spacetime is a smooth Killing horizon. We present a proof of this conjecture, under the assumption that the surface gravity of the horizon is a non-zero constant. The argument relies on two important observations: Firstly, the existence of a canonical null time function, associated to any horizon with constant non-zero surface gravity. Secondly, a unique continuation theorem for wave equations through smooth compact lightlike hypersurfaces, with constant non-zero surface gravity. We will also discuss what steps remain to prove the Moncrief-Isenberg conjecture and its relation to the classical black hole uniqueness conjecture.
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