Breaking an Abelian gauge symmetry near a black hole horizon

TL;DR

This paper proposes that coupling the Abelian Higgs model to gravity with a negative cosmological constant results in black holes that spontaneously break gauge symmetry through a charged scalar condensate near the horizon, implying black hole superconductivity.

Contribution

It introduces a model where black holes can spontaneously break gauge invariance, suggesting a new mechanism for black hole superconductivity in a gravitational setting.

Findings

Black holes can develop a charged scalar condensate outside the horizon.

Spontaneous gauge symmetry breaking occurs near black hole horizons.

Black holes can exhibit superconducting properties.

Abstract

I argue that coupling the Abelian Higgs model to gravity plus a negative cosmological constant leads to black holes which spontaneously break the gauge invariance via a charged scalar condensate slightly outside their horizon. This suggests that black holes can superconduct.