On visible effects in the double Schwarzschild solution

TL;DR

This paper investigates the visual effects caused by two black holes in a static Einstein solution, revealing how the Weyl strut influences light paths and how black hole separation affects observable phenomena.

Contribution

It provides a detailed analysis of null geodesics in the double Schwarzschild solution, highlighting the impact of the Weyl strut on light deflection and the differences based on black hole separation.

Findings

Weyl strut causes defocusing of light rays.

Large separation results in behavior similar to a single black hole.

Nearby black holes significantly alter null geodesic paths.

Abstract

Physical aspects of a static solution to the Einstein equations with two black holes 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 \emph{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 a widely changed behavior due to the Weyl strut.