Particle Moving around Two Extreme Black Holes

initial positions

ψ(0)

θ(0)

initial momenta

p

θ

(0)

p

ψ

(0)

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.