Black Hole Electromagnetic Duality

TL;DR

This paper explores electromagnetic duality in black hole physics, distinguishing between realizable and unrealizable dualities in various dimensions, and demonstrates their equivalence in charged black hole scenarios.

Contribution

It clarifies the nature of duality transformations in different dimensions and establishes their equivalence in the context of charged black holes with gravitational effects.

Findings

Duality transformations differ between dimensions 4k and 4k+2.

Certain dualities are realizable via dynamical generators in specific dimensions.

Electric and magnetic black holes exhibit equivalent actions under duality rotations.

Abstract

After defining the concept of duality in the context of general $n$-form abelian gauge fields in 2$n$ dimensions, we show by explicit example the difference between apparent but unrealizable duality transformations, namely those in $D=4k+2$, and those, in $D=4k$, that can be implemented by explicit dynamical generators. We then consider duality transformations in Maxwell theory in the presence of gravitation, particularly electrically and magnetically charged black hole geometries. By comparing actions in which both the dynamical variables and the charge parameters are "rotated," we show their equality for equally charged electric and magnetic black holes, thus establishing their equivalence for semiclassical processes which depend on the value of the action itself.