Homoclinic orbits around spinning black holes. II. The phase space portrait
Gabe Perez-GizPhysics Department, Columbia University, New York, New York 10027, USAJanna LevinDepartment of Physics and Astronomy, Barnard College of Columbia University, 3009 Broadway, New York, New York 10027, USA
2009en
ABI
Abstract
In paper I in this series, we found exact expressions for the equatorial homoclinic orbits: the separatrix between bound and plunging, whirling and not whirling motion. As a companion to that physical space study, in this paper we paint a phase space portrait of the homoclinic orbits that includes exact expressions for the actions and fundamental frequencies. Additionally, we develop a reduced Hamiltonian description of Kerr motion that allows us to track groups of trajectories with a single global clock. This facilitates a variational analysis, whose stability exponents and eigenvectors could potentially be useful for future studies of families of black hole orbits and their associated gravitational waveforms.
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