Thermodynamics of static dyonic AdS black holes in the $\omega$-deformed Kaluza-Klein gauged supergravity theory

TL;DR

This paper investigates the thermodynamics of static dyonic AdS black holes within an $$-dimensional $$-deformed Kaluza-Klein supergravity, revealing a necessary modification to the first law of thermodynamics through new conjugate variables.

Contribution

It introduces a modified first law for these black holes by identifying a new pair of thermodynamical variables using the quasi-local ADT formalism.

Findings

Modified first law with new conjugate variables (X, Y)

Verification of the new pair through quasi-local conserved charge calculation

Enhanced understanding of thermodynamics in $$-dimensional $$-deformed supergravity

Abstract

We study thermodynamical properties of static dyonic AdS black holes in four-dimensional $\omega$-deformed Kaluza-Klein gauged supergravity theory, and find that the differential first law requires a modification via introducing a new pair of thermodynamical conjugate variables (X, Y). To ensure such a modification, we then apply the quasi-local ADT formalism developed in Ref. [20] to calculate the quasi-local conserved charge and identify that the new pair is precisely the one previously introduced to modify the differential form of first law.