On equipotential photon surfaces in (electro-)static spacetimes of arbitrary dimension

08.02. bis 08.02.2022, 12:15-13:45  –  Room C9A03 Tübingen, 2.09.2.22 Campus Golm
Geometric Analysis, Differential Geometry and Relativity

Olivia Vicanek-Martinez

In my talk, we will study photon surfaces, namely timelike, umbilic hypersurfaces, in static, asymptotically flat, n + 1-dimensional spacetimes, possibly carrying a time-independent electric potential. First, I will give a complete characterization of all photon surfaces in a class of spherically symmetric spacetimes containing among others the (exterior) subextremal Reissner–Nordström spacetimes, and hence in particular the (exterior) positive mass Schwarzschild spacetimes (both of dimension n + 1 ≥ 4). Then I will show that (possibly disconnected) equipotential photon surfaces arising as the inner boundary of a static, asymptotically Reissner-Nordström, n+1-dimensional, electrovacuum spacetime forces the spacetime to be isometric to the (exterior) subextremal Reissner–Norström spacetime of the same mass and charge, where again n + 1 ≥ 4. The uniqueness result fundamentally relies on the lower regularity rigidity case of the (Riemannian) Positive Mass Theorem. This is joint work with Carla Cederbaum and Sophia Jahns.