Black holes and causal nonlinear electrodynamics

TL;DR

This paper explores how causality constraints in nonlinear electrodynamics affect the structure and phases of black hole solutions within Einstein-NLED theories, revealing new stability and phase properties.

Contribution

It demonstrates that causality restricts black hole solutions to specific phases and provides new insights into the stability and geometry of these solutions.

Findings

Equal-charge dyonic RN black holes are unstable in Born-type theories.

Causal theories have at most two horizons, leading to three possible phases.

Causality permits four distinct phase diagrams for black holes.

Abstract

For generic theories of nonlinear electrodynamics (NLED) we investigate the implications of (a)causality on spherically-symmetric solutions of the Einstein-NLED equations that are asymptotic to a Reissner-Nordstr\"om (RN) spacetime. Equal-charge dyonic RN black holes are shown to be exact, but unstable, solutions of (acausal) ``Born-type'' theories. For {\it all causal theories} it is shown that the metric is singular at the centre of symmetry and that it has at most two Killing horizons, implying at most three ``phases": RN-like or S(chwarzschild)-like black holes, and naked timelike singularities. For extreme RN-like black holes, including dyons, we give simple proofs of monotonicity conditions that imply a reduction of mass and entropy due to NLED interactions. We find that causality allows four qualitatively different phase-diagrams. One of the two with finite electromagnetic energy $\mathcal{E}_{\rm em}$ is the previously studied Born-Infeld-type, for which the zero-entropy limit of a ``small-charge" S-like black hole is a naked timelike singularity of mass $M=\mathcal{E}_{\rm em}$; we show that the spacetime geometry of this ``Born particle'' is that of the Bariola-Vilenkin global monopole.