Geometry of chaos in the two-center problem in General Relativity
arXiv:gr-qc/9412031 · doi:10.1103/PhysRevD.52.3176
Abstract
The now-famous Majumdar-Papapetrou exact solution of the Einstein-Maxwell equations describes, in general, static, maximally charged black holes balanced under mutual gravitational and electrostatic interaction. When , 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.
14 pages, 7 figures
References in corpus (1)
Cited by in corpus (31)
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