Static de-Sitter Black Holes Abhor Charged Scalar Hair

TL;DR

This paper proves a no-hair theorem for charged scalar fields around static black holes in de-Sitter space, extending previous results to more general couplings and higher curvature corrections, and excluding spontaneous scalarization.

Contribution

It establishes a general no charged scalar hair theorem for static de-Sitter black holes without symmetry restrictions, including non-minimal couplings and higher curvature terms.

Findings

No charged scalar hair exists for static de-Sitter black holes.

The theorem applies to non-spherical, non-minimal, and higher curvature scenarios.

Spontaneous scalarization of charged scalars is ruled out in this context.

Abstract

We prove a no charged scalar hair theorem for static black holes in de-Sitter spacetime in the region between the event horizon and the cosmological horizon. The proof does not depend on the assumption of spherical symmetry. It allows for general non-minimal coupling functions of the scalar field to gravity and electromagnetic fields, and for higher curvature term corrections to Einstein gravity. The extension to other asympitotic spacetimes is applicable by requiring appropriate boundary conditions. Our result excludes the possibility for spontaneous scalarization of charged scalar around static charged de-Sitter black holes.