# Spinning boson stars and hairy black holes with non-minimal coupling

## TL;DR

This paper constructs spinning boson stars and hairy black holes with non-minimal scalar-curvature coupling, demonstrating the universality of the synchronization mechanism and exploring their properties across different coupling regimes.

## Contribution

It presents new rotating solutions with non-minimal coupling, extending the understanding of hairy black holes and boson stars beyond minimal coupling models.

## Key findings

- Hairy black holes exist with non-minimal coupling, similar to minimal coupling cases.
- Physical properties of solutions are qualitatively unchanged by the coupling.
- No spherically symmetric hairy black holes exist under conformal regularity conditions.

## Abstract

We obtain spinning boson star solutions and hairy black holes with synchronised hair in the Einstein-Klein-Gordon model, wherein the scalar field is massive, complex and with a non-minimal coupling to the Ricci scalar. The existence of these hairy black holes in this model provides yet another manifestation of the universality of the synchronisation mechanism to endow spinning black holes with hair. We study the variation of the physical properties of the boson stars and hairy black holes with the coupling parameter between the scalar field and the curvature, showing that they are, qualitatively, identical to those in the minimally coupled case. By discussing the conformal transformation to the Einstein frame, we argue that the solutions herein provide new rotating boson star and hairy black hole solutions in the minimally coupled theory, with a particular potential, and that no spherically symmetric hairy black hole solutions exist in the non-minimally coupled theory, under a condition of conformal regularity.