Good tachyons, bad bradyons: role reversal in Einstein-nonlinear-electrodynamics models

TL;DR

This paper explores how nonlinear electrodynamics models coupled with Einstein's gravity can lead to unconventional particle behaviors, such as tachyons with good causal properties and black hole solutions that violate causality.

Contribution

It reveals a novel role reversal where photons can behave as tachyons and bradyons in nonlinear electrodynamics, depending on the field strength and Lagrangian properties.

Findings

Weak field limit shows good tachyons and bad bradyons.

Causality properties depend on the Lagrangian's concavity.

Certain regular black hole solutions are acausal.

Abstract

In relativistic mechanics, the 4-velocity and the 4-momentum need not be parallel. This allows their norm to have a different sign. This possibility occurs in nonlinear electrodynamics (NED) models minimally coupled to Einstein's theory. Surprisingly, for a large class of NED models with a Maxwell limit, for weak fields, the causal (acausal) photons, as determined by their 4-velocity, have a spacelike (timelike) 4-momentum, leading to good tachyons and bad bradyons. Departing from weak fields, this possibility is determined solely by the concavity of the NED Lagrangian, which is consistent with the Dominant Energy Condition analysis. As a corollary, some popular regular black hole solutions sourced by NED, such as the Bardeen and Hayward solutions, are acausal.