Fundamental photon orbits in the double Schwarzschild space-time

Abstract

We consider photon orbits in the space-time consisting of two identical Schwarzschild black holes in static equilibrium. In particular, we focus on fundamental photon orbits – bound photon orbits that do not fall into either black hole or go to infinity. It is known that there could exist up to two circular photon orbits lying in the plane of symmetry between the black holes. In this paper, we present more examples of fundamental photon orbits in this space-time. This includes non-circular orbits lying in the plane of symmetry, circular orbits that lie off the plane of symmetry, polar orbits, and non-planar orbits that orbit around one or both of the black holes. These orbits are all unstable. Finally, in an appendix, we present a class of circular time-like orbits that lie off the plane of symmetry.