Hairy black holes in scalar extended massive gravity

TL;DR

This paper constructs static, spherically symmetric black hole solutions with scalar hair in a ghost-free massive gravity extension, showing that asymptotically flat hairy black holes can exist without fine-tuning, unlike in bi-gravity models.

Contribution

It demonstrates the existence of hairy black holes in scalar extended massive gravity without fine-tuning parameters, expanding understanding of black hole solutions in modified gravity theories.

Findings

Asymptotically flat hairy black holes exist without fine-tuning.

Asymptotically AdS black holes can be obtained.

Asymptotically dS black holes are not found in the simplest models.

Abstract

We construct static, spherically symmetric black hole solutions in scalar extended ghost-free massive gravity and show the existence of hairy black holes in this class of extension. While the existence seems to be a generic feature, we focus on the simplest models of this extension and find that asymptotically flat hairy black holes can exist without fine-tuning the theory parameters, unlike the bi-gravity extension, where asymptotical flatness requires fine-tuning in the parameter space. Like the bi-gravity extension, we are unable to obtain asymptotically dS regular black holes in the simplest models considered, but it is possible to obtain asymptotically AdS black holes.