Geometry of chaos in the two-center problem in general relativity

Ulvi Yurtsever
Phys. Rev. D 52, 3176 – Published 15 September 1995
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Abstract

The now-famous Majumdar-Papapetrou exact solution of the Einstein-Maxwell equations describes, in general, N static, maximally charged black holes balanced under mutual gravitational and electrostatic interaction. When N=2, this solution defines the two-black-hole spacetime, and the relativistic two-center problem is the problem of geodesic motion on this static background. Contopoulos and a number of other workers have recently discovered through numerial experiments that, in contrast with the Newtonian two-center problem, where the dynamics is completely integrable, relativistic null-geodesic motion on the two-black-hole spacetime exhibits chaotic behavior Here I identify the geometric sources of this chaotic dynamics by first reducing the problem to that of geodesic motion on a negatively curved (Riemannian) surface.

  • Received 12 December 1994

DOI:https://doi.org/10.1103/PhysRevD.52.3176

©1995 American Physical Society

Authors & Affiliations

Ulvi Yurtsever

  • Jet Propulsion Laboratory 169-327, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California 91109
  • Theoretial Astrophysics 130-33, California Institute of Technology, Pasadena, California 91125

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Vol. 52, Iss. 6 — 15 September 1995

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