Kerr-Newman black holes with scalar hair

TL;DR

This paper constructs and analyzes new types of Kerr-Newman black holes with scalar hair, exploring both ungauged and gauged scalar fields, revealing modifications in electromagnetic properties and introducing new solitonic solutions.

Contribution

It presents the first explicit construction of Kerr-Newman black holes with scalar hair, including both ungauged and gauged cases, and analyzes their electromagnetic and physical properties.

Findings

Scalar hair does not affect the leading electric multipole moment.

Scalar hair suppresses the magnetic dipole moment, reducing the gyromagnetic ratio.

Gauged scalar fields introduce a new charged boson star limit.

Abstract

We construct electrically charged Kerr black holes (BHs) with scalar hair. Firstly, we take an uncharged scalar field, interacting with the electromagnetic field only indirectly, via the background metric. The corresponding family of solutions, dubbed Kerr-Newman BHs with ungauged scalar hair, reduces to (a sub-family of) Kerr-Newman BHs in the limit of vanishing scalar hair and to uncharged rotating boson stars in the limit of vanishing horizon. It adds one extra parameter to the uncharged solutions: the total electric charge. This leading electromagnetic multipole moment is unaffected by the scalar hair and can be computed by using Gauss's law on any closed 2-surface surrounding (a spatial section of) the event horizon. By contrast, the first sub-leading electromagnetic multipole -- the magnetic dipole moment --, gets suppressed by the scalar hair, such that the gyromagnetic ratio is always smaller than the Kerr-Newman value ($g=2$). Secondly, we consider a gauged scalar field and obtain a family of Kerr-Newman BHs with gauged scalar hair. The electrically charged scalar field now stores a part of the total electric charge, which can only be computed by applying Gauss' law at spatial infinity and introduces a new solitonic limit -- electrically charged rotating boson stars. In both cases, we analyse some physical properties of the solutions.