Geometry of chaos in the two center problem in general relativity

Dec, 1994
20 pages
Published in:
  • Phys.Rev.D 52 (1995) 3176-3183
e-Print:

Citations per year

1995200220092016202301234
Abstract: (arXiv)
The now-famous Majumdar-Papapetrou exact solution of the Einstein-Maxwell equations describes, in general, NN static, maximally charged black holes balanced under mutual gravitational and electrostatic interaction. When N=2N=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.
  • Einstein-Maxwell equation: solution
  • black hole
  • chaos
  • Riemann surface
  • numerical calculations