This Demonstration shows the geodesic motion of a particle with mass in the meridian plane for a metric corresponding to two extreme Reissner–Nordström black holes, where the Coulomb repulsion between them balances the Newtonian attraction. The solution obtained by Majumdar and Papapetrou is expressed here in prolate spheroidal coordinates. This is a version of the three-body problem in general relativity.

The equations of motion are derived from the metric

where

S. Chandrasekhar, "The Two-Centre Problem in General Relativity: The Scattering of Radiation by Two Extreme Reissner-Nordstrom Black Holes," Proc. R. Soc. Lond. A, 421(1861), 1989 pp. 227-258.