On the Photon Motion Near a Five-Dimensional Schwarzschild Black Hole

TL;DR

This paper explores photon trajectories near a five-dimensional Schwarzschild black hole, revealing unique singularities and proposing potential observational signatures of extra dimensions through photon bending behaviors.

Contribution

It introduces a new coordinate system to remove singularities and analyzes photon motion, highlighting possible signatures of extra spatial dimensions.

Findings

Identification of two time-coordinate singularities related to extra dimensions

Introduction of a new Regge-Wheeler tortoise coordinate to remove singularities

Simulation results suggest photon bending could indicate extra dimensions

Abstract

In this report, we discuss the dynamics of photons in a five-dimensional Schwarzschild black hole. We find that the corresponding Eddington-Finkelstein-like coordinate admits two time-coordinate singularities for a particular condition. This condition is due to the existence of a non-zero angular momentum related to the extra spatial dimension. By introducing a new Regge-Wheeler tortoise coordinate, both singularities can be removed from the Eddington-Finkelstein-like coordinate. It is identified that the additional singularity is related to the photon sphere in a hyperplane, and we analyze it using a dynamical system approach. Simulation results of photon motion based on numerical calculation are presented. It is suggested that the related bending motion characteristic can probably be considered as a signature for probing the existence of the extra spatial dimension.