Magnetic Field Probe of the No-Hair Theorem

TL;DR

This paper investigates how deviations from the no-hair theorem affect magnetic fields around black holes by analyzing deformed Kerr spacetimes and their electromagnetic signatures.

Contribution

It introduces a method to study magnetic field alterations caused by spacetime deformations that violate the no-hair theorem.

Findings

Deformation causes quadrupole-like corrections to magnetic fields.

Corrections are proportional to the deformation parameter.

Analysis is valid for slow-spinning black holes.

Abstract

We discuss the consequences of violating the no-hair theorem on magnetic fields surrounding a black hole. This is achieved by parametrically deforming the Kerr spacetime and studying the effects of such deformations on asymptotically uniform magnetic fields around the black hole. We compute the deformed electromagnetic field for slow spins and small deformation parameter, and show that the correction is of order the deformation parameter and mimics the angular structure of a quadrupole.