Non-Extremal Rotating Black Holes in Five-Dimensional Gauged Supergravity

TL;DR

The authors develop a unifying framework for non-extremal rotating black holes in five-dimensional gauged supergravity and construct the general single-charge solution with two independent rotations. They recast existing two- and three-charge gauged and ungauged solutions into this framework, providing compact expressions for metric and gauge fields and detailing thermodynamics, the BPS limit, and horizon structure. The work reveals separability of the Hamilton-Jacobi and Klein-Gordon equations in these backgrounds and establishes a foundation for extending to the full three-charge gauged case. This contributes a cohesive, algebraically transparent picture of rotating AdS black holes in five dimensions with potential implications for AdS/CFT and holographic thermodynamics.

Abstract

Supersymmetric black holes in five-dimensional gauged supergravity must necessarily be rotating, and so in order to study the passage to black holes away from supersymmetry, it is of great interest to obtain non-extremal black holes that again have non-zero rotation. In this paper we find a simple framework for describing non-extremal rotating black holes in five-dimensional gauged supergravities. Using this framework, we are able to construct a new solution, describing the general single-charge solution of N=2 gauged supergravity, with arbitrary values for the two rotation parameters. Previously-obtained solutions with two or three equal charges also assume a much simpler form in the new framework, as also does the general solution with three unequal charges in ungauged N=2 supergravity. We discuss the thermodynamics and BPS limit of the new single-charge solutions, and we discuss the separability of the Hamilton-Jacobi and Klein-Gordan equations in these backgrounds.