Scale Invariant Hairy Black Holes

TL;DR

This paper explores scalar fields coupled to 3D gravity, revealing a scaling symmetry that leads to a Smarr formula and establishing conditions for the existence of non-rotating hairy black holes, with extensions to higher dimensions.

Contribution

It uncovers a scaling symmetry in the black hole action and proves a Smarr formula applicable to any potential, also determining when hairy black holes can exist.

Findings

Scaling symmetry in black hole reduced action

Smarr formula valid for any potential

Non-rotating hairy black holes exist only for positive total energy

Abstract

Scalar fields coupled to three-dimensional gravity are considered. We uncover a scaling symmetry present in the black hole reduced action, and use it to prove a Smarr formula valid for any potential. We also prove that non-rotating hairy black holes exists only for positive total energy. The extension to higher dimensions is also considered.