No-Hair Theorem for Spontaneously Broken Abelian Models in Static Black Holes

TL;DR

This paper proves that in static black holes, spontaneously broken Abelian models cannot sustain electromagnetic fields outside the horizon, extending the no-hair theorem to these models with a gauge-invariant approach.

Contribution

It establishes a gauge-invariant proof that electromagnetic fields vanish in static black holes for spontaneously broken Abelian models, regardless of the specific model details.

Findings

Electromagnetic fields vanish outside static black holes in these models.

The proof is gauge invariant and model-independent.

In the Abelian Higgs model, only vacuum scalar field solutions are allowed.

Abstract

The vanishing of the electromagnetic field, for purely electric configurations of spontaneously broken Abelian models, is established in the domain of outer communications of a static asymptotically flat black hole. The proof is gauge invariant, and is accomplished without any dependence on the model. In the particular case of the Abelian Higgs model, it is shown that the only solutions admitted for the scalar field become the vacuum expectation values of the self-interaction.