Electric Charge in Interaction with Magnetically Charged Black Holes

TL;DR

This paper investigates the electromagnetic angular momentum of an electric charge near magnetically charged dilaton black holes, revealing how it varies with distance and approaches a constant in extremal cases, with implications for black hole physics.

Contribution

It demonstrates that electromagnetic angular momentum depends on separation distance and becomes independent near extremality, extending understanding across various black hole solutions.

Findings

Angular momentum depends on charge separation and decreases from eQ to 0.

Near extremality, angular momentum approaches eQ regardless of distance.

Features are expected to hold broadly in theories with complex field contents.

Abstract

We examine the angular momentum of an electric charge e placed at rest outside a dilaton black hole with magnetic charge Q. The electromagnetic angular momentum which is stored in the electromagnetic field outside the black hole shows several common features regardless of the dilaton coupling strength, though the dilaton black holes are drastically different in their spacetime structure depending on it. First, the electromagnetic angular momentum depends on the separation distance between the two objects and changes monotonically from eQ to 0 as the charge goes down from infinity to the horizon, if rotational effects of the black hole are discarded. Next, as the black hole approaches extremality, however, the electromagnetic angular momentum tends to be independent of the distance between the two objects. It is then precisely $eQ$ as in the electric charge and monopole system in flat spacetime. We discuss why these effects are exhibited and argue that the above features are to hold in widely generic settings including black hole solutions in theories with more complicated field contents, by addressing the no hair theorem for black holes and the phenomenon of field expulsion exhibited by extremal black holes.