Black holes and causal nonlinear electrodynamics

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.