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

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 $$D=5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> , $$\mathcal {N}= 2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> gauged supergravity coupled to three vector multiplets specified by the pre-potential $$\mathcal {V}= STU -W^2U \equiv 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>V</mml:mi> <mml:mo>=</mml:mo> <mml:mi>S</mml:mi> <mml:mi>T</mml:mi> <mml:mi>U</mml:mi> <mml:mo>-</mml:mo> <mml:msup> <mml:mi>W</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>U</mml:mi> <mml:mo>≡</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> . 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 $$_5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>5</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> 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.