Using the Uncharged Kerr Black Hole as a Gravitational Mirror

TL;DR

This paper explores how uncharged Kerr black holes can act as gravitational mirrors by analyzing null geodesics, deriving conditions for boomerang photons, and numerically illustrating their trajectories.

Contribution

It extends previous work on Schwarzschild black holes to Kerr black holes, deriving new equations and conditions for boomerang photon trajectories.

Findings

Conditions for boomerang photon existence derived

Equations for emission angles established

Numerical simulations illustrate photon trajectories

Abstract

We extend the study of the possibility to use the Schwarzschild black hole as a gravitational mirror to the more general case of an uncharged Kerr black hole. We use the null geodesic equation in the equatorial plane to prove a theorem concerning the conditions the impact parameter has to satisfy if there shall exist boomerang photons. We derive an equation for these boomerang photons and an equation for the emission angle. Finally, the radial null geodesic equation is integrated numerically in order to illustrate boomerang photons.