Causality of Photon Propagation under Dominant Energy Condition in Non-linear Electrodynamics

TL;DR

This paper investigates how the causality of photon propagation in nonlinear electrodynamics relates to the dominant energy condition, showing that DEC violation allows for faster-than-light photon trajectories in certain black hole spacetimes.

Contribution

It establishes a link between photon causality and the dominant energy condition in static, spherically symmetric NED black hole solutions, highlighting conditions for superluminal photon propagation.

Findings

DEC always satisfied when photon trajectories are timelike with angular momentum.

Violation of DEC permits faster-than-light photon propagation.

Results hold in weak field limit for NED with Maxwell limit.

Abstract

Recently, various types of regular black hole model are reintroduced as the solution of the Einstein equations coupled with nonlinear electrodynamics (NED). In NED, it is known that photons do not propagate along the null geodesics of the spacetime geometry, but of so-called effective geometry, which suggests the possibility of so-called ``faster/slower than light" photons. We study the relation between the causality of photons and the dominant energy condition (DEC) in some static and spherically symmetric black hole spacetimes in NED. We show that if photon trajectories with a nonzero angular momentum are timelike in the spacetime geometry, DEC is always satisfied in static and spherically symmetric spacetimes in any NED that admits the Maxwell limit, and vice versa, at least, in the weak field limit. Thus, this implies that in such NED, the violation of DEC admits the existence of faster than light photons.