General Nonextremal Rotating Charged AdS Black Holes in Five-dimensional $U(1)^3$ Gauged Supergravity: A Simple Construction Method

TL;DR

This work tackles the long-standing problem of obtaining the most general nonextremal rotating charged AdS$_5$ black hole in five-dimensional $U(1)^3$ gauged supergravity. It introduces a universal metric ansatz, built on a generalization of a single-charge construction, and a simple four-step algorithm to derive a complete solution with two unequal rotations and three independent charges, along with the gauge fields and scalars. The resulting solution, expressed in closed form, reduces to previously known Kerr-AdS$_5$ and Cvetič-Youm configurations in appropriate limits and has its conserved charges and thermodynamics explicitly computed, satisfying the first-law of thermodynamics. The method provides a unifying framework for gauged and ungauged cases and holds promise for extending to other theories and horizon topologies, with direct relevance to $AdS_5/ CFT_4$ tests in M-theory.

Abstract

With the help of a generalized form of the metric ansatz found for the single-charge case in a previous work [S.Q. Wu, Phys. Rev. D 83, 121502(R) (2011)], I adopt a simple algorithm to construct the most general nonextremal rotating charged black hole solutions in five-dimensional $U(1)^3$ gauged supergravity. The general solution that is interesting for testing the AdS$_5$/CFT$_4$ correspondence in M-theory, is characterized by its mass, two unequal rotation parameters, three different U(1) charges, and a negative cosmological constant. The metric ansatz is very universal and illuminative, it is not only especially suitable for constructing solutions with multiple different electric charges in (un)gauged supergravities, but also for other dilatonic gravity theory.