Uniqueness of Rotating Charged Black Holes in Five-Dimensional Minimal Gauged Supergravity

TL;DR

This paper proves the uniqueness of a specific five-dimensional rotating charged black hole solution in minimal gauged supergravity, under certain torsion and conformal Killing-Yano form conditions.

Contribution

It establishes the uniqueness of the Chong-Cvetic-Lu-Pope black hole solution in five-dimensional minimal gauged supergravity with torsion and conformal Killing-Yano 2-form assumptions.

Findings

Proves the spacetime is uniquely given by the Chong-Cvetic-Lu-Pope solution.

Identifies conditions under which the black hole solution is unique.

Demonstrates the role of torsion and conformal Killing-Yano forms in black hole uniqueness.

Abstract

We study a five-dimensional spacetime admitting, in the presence of torsion, a non-degenerate conformal Killing-Yano 2-form which is closed with respect to both the usual exterior differentiation and the exterior differentiation with torsion. Furthermore, assuming that the torsion is closed and co-closed with respect to the exterior differentiation with torsion, we prove that such a spacetime is the only spacetime given by the Chong-Cvetic-Lu-Pope solution for stationary, rotating charged black holes with two independent angular momenta in five-dimensional minimal gauged supergravity.