
Physics 1994
Geometry of chaos in the twocenter problem in General RelativityAbstract: The nowfamous MajumdarPapapetrou exact solution of the EinsteinMaxwell equations describes, in general, $N$ static, maximally charged black holes balanced under mutual gravitational and electrostatic interaction. When $N=2$, this solution defines the twoblackhole spacetime, and the relativistic twocenter 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 twocenter problem, where the dynamics is completely integrable, relativistic nullgeodesic motion on the two blackhole 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.
