Phys. Rev. D 79, 124014 (2009) [11 pages]

Homoclinic orbits around spinning black holes. II. The phase space portrait

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Gabe Perez-Giz^1,* and Janna Levin^2,3,†
¹Physics Department, Columbia University, New York, New York 10027, USA
²Department of Physics and Astronomy, Barnard College of Columbia University, 3009 Broadway, New York, New York 10027, USA
³Institute for Strings, Cosmology and Astroparticle Physics, Columbia University, New York, New York 10027, USA

Received 2 December 2008; published 11 June 2009

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.

URL:

http://link.aps.org/doi/10.1103/PhysRevD.79.124014

DOI:

10.1103/PhysRevD.79.124014

PACS:

04.70.−s, 95.30.Sf, 04.25.−g, 04.20.Jb

^*gabe@phys.columbia.edu

^†janna@astro.columbia.edu

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Phys. Rev. D 79, 124014 (2009) [11 pages]

Homoclinic orbits around spinning black holes. II. The phase space portrait

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