Geometry of chaos in the two-center problem in General Relativity

Details Geometry of chaos in the two-center problem in General Relativity Geometry of chaos in the two-center problem in General Relativity

1994-12-10

arxiv.org/abs/gr-qc/9412031v1

Phys.Rev.D52:3176-3183,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, 7 figures

Scientific paper

10.1103/PhysRevD.52.3176

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 numerical 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.

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