Thermodynamics and topological classifications of static non-extremal four-charge AdS black hole in the five-dimensional $\mathcal{N} = 2$, $STU-W^2U$ gauged supergravity

TL;DR

This paper explores the thermodynamics and topological aspects of a novel five-dimensional AdS black hole with four electric charges in gauged supergravity, confirming consistent thermodynamic relations and linking to known models.

Contribution

It introduces a new four-charge non-extremal AdS black hole solution in five-dimensional gauged supergravity and analyzes its thermodynamics and topological classifications.

Findings

Thermodynamics satisfies both differential and integral mass formulas.

Reduces to known three-charge black hole when one charge is zero.

Provides insights into topological classifications of black hole thermodynamics.

Abstract

In this paper, we investigate thermodynamical aspects of a novel static non-extremal black hole solution in the five-dimensional anti-de Sitter (AdS) space carrying four independent electric charge parameters and with a negative cosmological constant, within the framework of $D=5$, $\mathcal{N} = 2$ gauged supergravity coupled to three vector multiplets specified by the pre-potential $\mathcal{V} = STU -W^2U \equiv 1$. A central outcome of our work is the demonstration that the thermodynamics of this solution consistently satisfies both the differential and integral forms of the mass formulae of black hole thermodynamics. When the fourth charge is set to zero, our configuration reduces to the known three-charge static non-extremal AdS$_5$ black hole within the gauged $STU$ model, and its thermodynamic behavior connects smoothly to that limit. Finally, we also provide a brief discussion about topological classifications of its thermodynamics.