KAM and Geodesic Dynamics of Blackholes

Abstract

In this paper we apply KAM theory and the Aubry-Mather theory for twist maps to the study of bound geodesic dynamics of a perturbed blackhole background. The general theories apply mainly to two observable phenomena: the photon shell (unstable bound spherical orbits) and the quasi-periodic oscillations (QPO). We prove that there is a gap structure in the photon shell that can be used to reveal information of the perturbation.