Can a light ray distinguish charge of a black hole in nonlinear electrodynamics?

TL;DR

This paper investigates whether light ray trajectories can differentiate between electric and magnetic charges of black holes in nonlinear electrodynamics, concluding that they cannot distinguish the charge type based on light motion.

Contribution

It demonstrates that light rays cannot be used to determine whether a black hole's charge is electric or magnetic in nonlinear electrodynamics.

Findings

Light rays follow effective space-time geodesics, not the original space-time.

The motion of light rays cannot distinguish electric from magnetic charges.

Results apply to black holes in general relativity coupled with nonlinear electrodynamics.

Abstract

It is a well-known fact that light rays do not follow the null geodesics of the space-time in nonlinear electrodynamics; instead, they follow the null geodesics of the so-called effective space-time. Taking this into account, in this paper, we aim to discuss the possibility of distinguishing the type of charge with which the black hole is endowed, via the motion of light rays. The results show that, for any black hole being a charged solution of the field equations of general relativity coupled to the nonlinear electrodynamics, one cannot distinguish the two types of charge (magnetic or electric) through the motion of light rays around it.