Relativistic Euler's 3-body problem, optical geometry and the golden ratio

Understand

A Weyl solution describing two Schwarzschild black holes is considered.

• We focus on the Z_2 invariant solution, with ADM mass M_{ADM}=2M_K, where M_K is the Komar mass of each black hole.
• For this solution the set of fixed points of the discrete symmetry is a totally geodesic sub-manifold.
• The existence and radii of circular photon orbits in this sub-manifold are studied, as functions of the distance 2L between the two black holes.