Embedding hairy black holes in a magnetic universe

TL;DR

This paper extends Ernst's solution generating technique to Einstein-Maxwell-scalar theories, enabling the construction of new solutions like hairy black holes embedded in a magnetic universe, revealing the rich structure of these configurations.

Contribution

It adapts Ernst's method to scalar-coupled Einstein-Maxwell theory and demonstrates how to embed hairy black holes into a magnetic universe using Kinnersley transformations.

Findings

Constructed new solutions with scalar hair in magnetic universes.

Demonstrated the integrability and symmetry properties of the extended system.

Provided explicit examples of hairy black holes embedded in magnetic fields.

Abstract

Ernst's solution generating technique is adapted to Einstein-Maxwell theory conformally (and minimally) coupled to a scalar field. This integrable system enjoys a SU(2,1) symmetry which enables one to move, by Kinnersley transformations, though the axisymmetric and stationary solution space, building an infinite tower of physically inequivalent solutions. As a specific application, metrics associated to scalar hairy black holes, such as the ones discovered by Bocharova, Bronnikov, Melnikov and Bekenstein, are embedded in the external magnetic field of the Melvin universe.