Instability of nonsingular black holes in nonlinear electrodynamics

TL;DR

This paper demonstrates that nonsingular black holes in nonlinear electrodynamics are inherently unstable near their centers due to negative squared sound speed, implying such stable solutions likely require alternative theories.

Contribution

It reveals the universal Laplacian instability of nonsingular black holes in nonlinear electrodynamics, challenging their viability as stable models.

Findings

Nonsingular black holes in nonlinear electrodynamics are unstable near the center.

Instability arises from negative squared sound speed in the angular direction.

Perturbations lead to the breakdown of the regular black hole metric.

Abstract

We show that nonsingular black holes realized in nonlinear electrodynamics are always prone to Laplacian instability around the center because of a negative squared sound speed in the angular direction. This is the case for both electric and magnetic BHs, where the instability of one of the vector-field perturbations leads to enhancing a dynamical gravitational perturbation in the even-parity sector. Thus, the background regular metric is no longer maintained in a steady state. Our results suggest that the construction of stable, nonsingular black holes with regular centers, if they exist, requires theories beyond nonlinear electrodynamics.