12.12.2024, 16:15
– Raum 0.14
Forschungsseminar Differentialgeometrie
First steps towards an equivariant Lorentzian index theorem
Lennart Ronge (UP)
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.
Access data at:https://moodle2.uni-potsdam.de/course/view.php?id=24418