# Kerr black holes with synchronised scalar hair and boson stars in the Einstein-Friedberg-Lee-Sirlin model

## TL;DR

This paper introduces a new family of rotating boson stars and hairy black holes in a two-component scalar field model coupled to gravity, exploring their properties and similarities to known solutions.

## Contribution

It presents the first study of axially-symmetric, rotating boson stars and black holes with scalar hair in the Friedberg-Lee-Sirlin model coupled to Einstein gravity.

## Key findings

- Existence of spinning hairy black holes with scalar hair.
- Close similarity to Kerr black holes with scalar hair.
- Solutions interpolate between boson stars and known scalar field black holes.

## Abstract

We study a new family of self-gravitating axially-symmetric, rotating boson stars in the two-component Friedberg-Lee-Sirlin model minimally coupled to Einstein gravity in four spacetime dimensions. In the flat space limit the boson stars tend to the corresponding Q-balls. Subject to the usual synchronization condition, the model admits spinning hairy black hole solutions with two different types of scalar hair. We here investigate parity-even and parity-odd boson stars and their associated hairy black holes. We explore the domain of existence of the solutions and address some of their physical properties. The solutions exhibit close similarity to the corresponding boson stars and Kerr black holes with synchronised scalar hair in the $O(3)$-sigma model coupled to Einstein gravity and to the corresponding solutions in the Einstein-Klein-Gordon theory with a complex scalar field, where the latter are recovered in a limit.