Abstract
A Weyl solution describing two Schwarzschild black holes is considered. We focus on the invariant solution, with Arnowitt-Deser-Misner mass , where is the Komar mass of each black hole. For this solution the set of fixed points of the discrete symmetry is a totally geodesic submanifold. The existence and radii of circular photon orbits in this submanifold are studied, as functions of the distance between the two black holes. For there are two such orbits, corresponding to and in Schwarzschild coordinates. As the distance increases, it is shown that the two photon orbits approach one another and merge when , where is the golden ratio. Beyond this distance there exist no circular photon orbits. The two null orbits delimit a forbidden band for timelike circular orbits, which is interpreted in terms of optical geometry. For large , timelike circular orbits are allowed everywhere, as in the analogous Newtonian problem. The analysis is generalized by considering a invariant Weyl solution with an array of black holes and also by charging the black holes, which connects the Weyl solution to a Majumdar-Papapetrou spacetime.
1 More- Received 28 September 2009
DOI:https://doi.org/10.1103/PhysRevD.80.104036
©2009 American Physical Society