No hair theorems for positive \Lambda

TL;DR

This paper extends black hole no-hair theorems to spacetimes with positive cosmological constant, showing limitations on supporting scalar and vector fields, and exploring quantum hair and charged solutions.

Contribution

It generalizes existing no-hair theorems to include positive , and introduces new results on quantum hair and specific charged solutions.

Findings

Static spherical black holes with >0 cannot support scalar fields in convex potentials.

Such black holes cannot support Proca-massive vector fields between horizons.

Existence of at least one quantum hair and exactly one charged solution in the Abelian Higgs model.

Abstract

We extend all known black hole no-hair theorems to space-times endowed with a positive cosmological constant $\Lambda.$ Specifically, we prove that static spherical black holes with $\Lambda>0$ cannot support scalar fields in convex potentials and Proca-massive vector fields in the region between black hole and cosmic horizons. We also demonstrate the existence of at least one type of quantum hair, and of exactly one charged solution for the Abelian Higgs model. Our method of proof can be applied to investigate other types of quantum or topological hair on black holes in the presence of a positive $\Lambda.$