Black holes and causal nonlinear electrodynamics

Abstract

A bstract 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-Nordström (RN) spacetime. Equal-charge dyonic RN black holes are shown to be exact, but unstable, solutions of (acausal) “Born-type” theories. For 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 ℰ 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 = ℰ em ; we show that the spacetime geometry of this “Born particle” is that of the Bariola-Vilenkin global monopole.