Closed null geodesic found by symmetry in eight charged black holes arranged on a cube
The Majumdar-Papapetrou solution to the Einstein-Maxwell equations describes a collection of extremally charged black holes in electrostatic equilibrium. Here eight such black holes are arranged on the vertices of a cube. The symmetries of this configuration confine some light rays to a plane through the cube’s center: numerically searching over initial conditions on this subspace reveals the existence of a closed null geodesic — a light ray that returns exactly to its starting point.
The geodesics are computed by numerical integration in the Majumdar-Papapetrou metric with potential U=1+∑i=18Mi/∣x−xi∣. Controls: Click and drag to orbit, scroll to zoom.
