Geometry Seminar: A. Ellithy
Speaker: Ahmed Ellithy, Uppsala University
Title: The Spacetime Penrose Inequality under a Quasi Final State Hypothesis
Abstract:
Penrose's heuristic argument for the spacetime Penrose inequality is fundamentally dynamical: the area of an apparent horizon should be compared with the mass measured at infinity after the black-hole exterior has settled down to Kerr. In this talk, I will explain how this heuristic can be made precise under a \emph{quasi-final-state} assumption, a late-time hypothesis which asks for much less than convergence of the spacetime to Kerr.
The main new geometric ingredient is the definition of a tangentially maximal hypersurface. These are spacelike hypersurfaces foliated by spheres with vanishing timelike mean curvature. Their construction is governed by a quasilinear inward-parabolic equation, for which we develop the corresponding a priori theory and prove global existence in the late-time region of the spacetime. I will then explain how the existence of these hypersurfaces reduce the spacetime Penrose inequality to the Riemannian Penrose Inequality.