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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. We discover there is a gap structure in the photon shell that can be used to reveal information of the perturbation.
In this paper, we study the chaotic motion of a massive particle moving in a perturbed Schwarzschild or Kerr background. We discover three novel orbits that do not exist in the unperturbed cases. First, we find zoom-whirl orbits moving around the pho
We prove an analytic KAM-Theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the theorem present
For scalar, electromagnetic, or gravitational wave propagation on a fixed Schwarzschild blackhole background, we describe the exact nonlocal radiation outer boundary conditions (ROBC) appropriate for a spherical outer boundary of finite radius enclos
Within the framework of Geodesic Brane Gravity, the deviation from General Relativity is parameterized by the conserved bulk energy. The corresponding geodesic evolution/nucleation of a de-Sitter brane is shown to be exclusively driven by a double-we
We classify radial timelike geodesic motion of the exterior non-extremal Kerr spacetime by performing a taxonomy of inequivalent root structures of the first order radial geodesic equation using a novel compact notation and by implementing the constr