Homoclinic orbits around spinning black holes. I. Exact solution for the Kerr separatrix

Janna Levin and Gabe Perez-Giz
Phys. Rev. D 79, 124013 – Published 11 June 2009

Abstract

For equatorial Kerr orbits, we show that each separatrix between bound and plunging geodesics is a homoclinic orbit—an orbit that asymptotes to an energetically-bound, unstable circular orbit. We derive exact expressions for these trajectories in terms of elementary functions. We also clarify the formal connection between the separatrix and zoom-whirl orbits and show that, contrary to popular belief, zoom-whirl behavior is not intrinsically a near-separatrix phenomenon. This paper focuses on homoclinic behavior in physical space, while in a companion paper we paint the complementary phase space portrait. Although they refer to geodesic motion, the exact solutions for the Kerr separatrix could be useful for analytic or numerical studies of eccentric transitions from orbital to plunging motion under the dissipative effects of gravitational radiation.

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  • Received 2 December 2008

DOI:https://doi.org/10.1103/PhysRevD.79.124013

©2009 American Physical Society

Authors & Affiliations

Janna Levin1,2,* and Gabe Perez-Giz3,†

  • 1Department of Physics and Astronomy, Barnard College of Columbia University, 3009 Broadway, New York, New York 10027, USA
  • 2Institute for Strings, Cosmology and Astroparticle Physics, Columbia University, New York, New York 10027, USA
  • 3Physics Department, Columbia University, New York, New York 10027, USA

  • *janna@astro.columbia.edu
  • gabe@phys.columbia.edu

See Also

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

Gabe Perez-Giz and Janna Levin
Phys. Rev. D 79, 124014 (2009)

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Issue

Vol. 79, Iss. 12 — 15 June 2009

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