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    Visible effects in the double Schwarzschild solution

    Eddy Brandon de León1,*, Jörg Frauendiener2,†, and Christian Klein3,4,‡

    • 1Department of Mathematics, Boltzmannstrasse 3, TU München, D-85748 Garching bei München, Germany
    • 2Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin 9054, New Zealand
    • 3Université Bourgogne Europe, CNRS, IMB UMR 5584, 21000 Dijon, France
    • 4Institut Universitaire de France

    • *Contact author: eddy.de.leon@tum.de
    • †Contact author: joerg.frauendiener@otago.ac.nz
    • ‡Contact author: christian.klein@u-bourgogne.fr

    Phys. Rev. D 114, 024040 – Published 17 July, 2026

    DOI: https://doi.org/10.1103/dqwp-6pqn

    Abstract

    Physical aspects of a static solution to the Einstein equations with two black holes of equal mass are studied via ray tracing. The exact solution for this double Schwarzschild solution is known in explicit form. The black holes are separated by a singularity called Weyl strut. The effect of this strut on null geodesics is shown to be defocusing, in contrast to the focusing effect of the black holes. It is shown that black holes with a large separation essentially lead to similar behavior of the null geodesics as a single black hole, whereas nearby holes display widely changed behavior due to the Weyl strut.

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