2009/09/24 by Flávio S. Coelho, Flavio S. Coelho, Carlos A. R. Herdeiro +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Circular orbit #Classical mechanics #General relativity #Geodesic #Geometry #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Relativity and Gravitational Theory #Schwarzschild metric #Schwarzschild radius #Spacetime #Submanifold #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.80.104036
published as Phys.Rev.D80:104036,2009 · 16 pages, 8 figures
arxiv created 2009/09/24 · openalex publication_date 2009/11/30 · arxiv updated 2010/04/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A Weyl solution describing two Schwarzschild black holes is considered. We focus on the ℤ2 invariant solution, with Arnowitt-Deser-Misner mass MADM=2MK, where MK 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 2L between the two black holes. For L\ensuremath→0 there are two such orbits, corresponding to r=3MADM and r=2MADM in Schwarzschild coordinates. As the distance increases, it is shown that the two photon orbits approach one another and merge when MK=\ensuremathφL, where \ensuremathφ 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 L, timelike circular orbits are allowed everywhere, as in the analogous Newtonian problem. The analysis is generalized by considering a ℤ2 invariant Weyl solution with an array of N black holes and also by charging the black holes, which connects the Weyl solution to a Majumdar-Papapetrou spacetime.