Excising Cauchy Horizons with Nonlinear Electrodynamics

TL;DR

This paper shows that nonlinear electrodynamics can remove Cauchy horizons in charged black holes, replacing them with regular black holes with a single event horizon and a spacelike singularity, thus restoring predictability.

Contribution

It demonstrates that regularizing point charge self-energy via nonlinear electrodynamics eliminates Cauchy horizons in weakly charged black holes, providing a new perspective on black hole structure.

Findings

Cauchy horizons are absent in regularized nonlinear electrodynamics black holes.

Born-Infeld electrodynamics sets an upper charge bound for black holes.

Regularized black holes resemble Schwarzschild black holes with a single horizon.

Abstract

Charged and/or rotating black holes in General Relativity feature Cauchy horizons, which indicate a breakdown of predictability in the theory. Focusing on spherically symmetric charged black holes, we remark that the inevitability of Reissner-Nordstrom Cauchy horizon is due to the divergent electromagnetic self-energy of point charges. We demonstrate that any causal theory of nonlinear electrodynamics that regularizes the point charge self-energy also eliminates Cauchy horizons for weakly charged black holes. These black holes feature one (event) horizon and a spacelike singularity, analogous to the Schwarzschild metric. An example with Born-Infeld electrodynamics illustrates how this gives rise to an upper bound on the charge, which we compare with known bounds.