No hair theorem in quasi-dilaton massive gravity

TL;DR

This paper demonstrates that in quasi-dilaton massive gravity, static, spherically symmetric black holes only exist under fine-tuned conditions, resulting in solutions identical to those in general relativity with no additional scalar hair.

Contribution

It shows that black hole solutions in quasi-dilaton massive gravity require fine-tuning and are equivalent to GR solutions, establishing a no hair theorem in this context.

Findings

Black hole solutions exist only with fine-tuning of parameters.

Solutions are identical to general relativity black holes.

No scalar hair exists for these black holes.

Abstract

We investigate the static, spherically symmetric black hole solutions in the quasi-dilaton model and its generalizations, which are scalar extended dRGT massive gravity with a shift symmetry. We show that, unlike generic scalar extended massive gravity models, these theories do not admit static, spherically symmetric black hole solutions until the theory parameters in the dRGT potential is fine-tuned. When fine-tuned, the geometry of the static, spherically symmetric black hole is necessarily that of general relativity and the quasi-dilaton field is constant across the spacetime. The fine-tuning and the no hair theorem apply to black holes with flat, anti-de Sitter or de Sitter asymptotics.