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