Uniqueness theorems for Kaluza-Klein black holes in five-dimensional minimal supergravity

TL;DR

This paper proves uniqueness theorems for five-dimensional Kaluza-Klein black holes in minimal supergravity, showing they are characterized by a specific set of physical parameters under certain symmetry and topological conditions.

Contribution

It establishes the first comprehensive uniqueness theorems for charged rotating black holes and black rings in five-dimensional minimal supergravity with specified symmetries and horizon topologies.

Findings

Black holes are uniquely characterized by mass, angular momenta, electric charge, magnetic flux, and nut charge.

Black rings, if they exist, are uniquely determined by dipole charge and rod structure.

Theorems apply under assumptions of axial symmetries and specific horizon topologies.

Abstract

We show uniqueness theorems for Kaluza-Klein black holes in the bosonic sector of five-dimensional minimal supergravity. More precisely, under the assumptions of the existence of two commuting axial isometries and a non-degenerate connected event horizon of the cross section topology S^3, or lens space, we prove that a stationary charged rotating Kaluza-Klein black hole in five-dimensional minimal supergravity is uniquely characterized by its mass, two independent angular momenta, electric charge, magnetic flux and nut charge, provided that there does not exist any nuts in the domain of outer communication. We also show that under the assumptions of the same symmetry, same asymptotics and the horizon cross section of S^1\times S^2, a black ring within the same theory---if exists---is uniquely determined by its dipole charge and rod structure besides the charges and magnetic flux.