Towards a Novel no-hair Theorem for Black Holes

TL;DR

This paper presents numerical evidence for a new no-scalar-hair theorem in general relativity, showing static black holes cannot have spherical scalar hair if the scalar field theory satisfies the Positive Energy Theorem, with implications for string theory compactifications.

Contribution

It introduces a novel no-scalar-hair theorem applicable to static black holes under specific energy conditions, extending understanding of black hole uniqueness in scalar-tensor theories.

Findings

No-scalar-hair theorem holds when the Positive Energy Theorem is satisfied.

The theorem applies to theories with scalar potentials having negative regions, under certain asymptotic symmetries.

Numerical evidence supports the theorem's validity in various scenarios.

Abstract

We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.