18/04/2018, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Oliver Lindblad Petersen, University of Potsdam
Wave equations with initial data on compact Cauchy horizons
I will present a new energy estimate for wave equations close to compact non-degenerate Cauchy horizons. The estimate allows one to conclude several existence and uniqueness results for wave equations with initial data on the Cauchy horizon. This generalizes classical results that were proven under the assumption of either analyticity or symmetry of the spacetime or closedness of the generators. In particular, the results are useful in understanding the geometry of vacuum spacetimes with a compact non-degenerate Cauchy horizon (without making any extra assumptions). This problem is closely related to the strong cosmic censorship conjecture.