A Monopole Near a Black Hole

TL;DR

This paper investigates how an electric charge near a magnetically charged black hole affects the spacetime geometry, showing that the system's external appearance aligns with known black hole solutions and confirming the no-hair theorem.

Contribution

It demonstrates that a charge near a magnetic black hole results in an exterior geometry equivalent to a Kerr-Newman black hole, confirming the no-hair theorem in this context.

Findings

Exterior geometry approaches Kerr-Newman form at large distances

Charge crossing the horizon results in a rotating Kerr-Newman black hole

Angular momentum matches the standard value for a monopole pair

Abstract

We study an electric charge held at rest outside a magnetically charged black hole. We find that even if the electric charge is treated as a perturbation on a spherically symmetric magnetic Reissner-Nordstrom hole, the geometry at large distances is that of a magnetic Kerr-Newman black hole. When the charge approaches the horizon and crosses it, the exterior geometry becomes that of a Kerr-Newman hole with electric and magnetic charges and with total angular momentum given by the standard value for a charged monopole pair. Thus, in accordance with the "no-hair theorem", once the charge is captured by the black hole, the angular momentum associated with the charge monopole system, looses all traces of its exotic origin and it is perceived from the outside as common rotation. It is argued that a similar analysis performed on Taub-NUT space should give the same result, namely, if one holds an ordinary mass outside of the horizon of a Taub-NUT space with only magnetic mass, the system, as seen from large distances, is endowed with an angular momentum proportional to the product of the two kinds of masses. When the ordinary, electric, mass reaches the horizon, the exterior metric becomes that of a rotating Taub-NUT space.