Trapping of light in stationary spacetimes

Abstract

We study phenomena related to trapping of light in stationary spacetimes. We first prove a uniqueness result for ‘quasilocal photon spheres‘ and static horizons in asymptotically flat so-called pseudo-electrostatic systems. Our result implies that an asymptotically Reissner--Nordström electrostatic system of arbitrary dimension which contains a ‘subextremal‘ photon sphere is a Reissner--Nordström manifold. The methods used in the proof of this theorem go back to the classical black hole uniqueness proofs of Bunting and Masood-ul-Alam and Ruback, whose techniques we combine with newer ideas developed by Cederbaum--Galloway and Cederbaum. In the second part, we leave the static setting and investigate trapped light in the Kerr spacetime. We give a new and (compared an earlier result by Dyatlov) more direct proof that the photon region in the Kerr spacetime can be naturally understood as a submanifold of the phase space and has topology SO(3)xR.