Uniqueness of photon spheres via positive mass rigidity
Differential Geometry
2015-12-15 v2 General Relativity and Quantum Cosmology
Analysis of PDEs
Abstract
In a recent paper the first author established the uniqueness of photon spheres, suitably defined, in static vacuum asymptotically flat spacetimes by adapting Israel's proof of static black hole uniqueness. In this note we establish uniqueness of photon spheres by adapting the argument of Bunting and Masood-ul-Alam, which then allows certain assumptions to be relaxed. In particular, multiple photon spheres are allowed a priori. As a consequence of our result, we can rule out the existence of static configurations involving multiple "very compact" bodies and black holes.
Keywords
Cite
@article{arxiv.1504.05804,
title = {Uniqueness of photon spheres via positive mass rigidity},
author = {Carla Cederbaum and Gregory J. Galloway},
journal= {arXiv preprint arXiv:1504.05804},
year = {2015}
}
Comments
minor changes; to appear in Commun. in Analysis and Geometry