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arXiv · 0811.3815

Homoclinic Orbits around Spinning Black Holes II: The Phase Space Portrait

Gabe Perez-Giz·Janna Levin
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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. 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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Gabe Perez-Giz, Janna Levin. 2008-11-24. Homoclinic Orbits around Spinning Black Holes II: The Phase Space Portrait. https://doi.org/10.1103/physrevd.79.124014

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