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arXiv · 2606.26210

Extended Thermodynamics and Throttling Process of Charged AdS Black Holes in ModMax-dRGT Massive Gravity with Sharma-Mittal Entropy

Naba Jyoti Gogoi·Hassan Hassanabadi·Himasri Pinapothu·Dhruba Jyoti Gogoi
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Abstract

We investigate the extended thermodynamics, including the Joule-Thomson expansion and $P-V$ criticality, of a four-dimensional charged anti-de Sitter (AdS) black hole within the combined framework of ModMax nonlinear electrodynamics and dRGT-like massive gravity. Operating in the extended phase space and employing the generalised Sharma-Mittal entropy to account for non-extensive statistical correlations, we derive exact analytical expressions for the modified Hawking temperature, specific heat, Joule-Thomson coefficient, and the equation of state. Our analysis of the throttling process reveals that the conformal nonlinearities of the ModMax field ($\gamma$) expand the physically accessible cooling domain by shifting the inversion transition to smaller horizon radii. While the Sharma-Mittal parameters ($\delta$, $R$) critically govern local thermodynamic stability and the inversion radius, the global inversion phase boundary remains fundamentally dictated by the massive graviton background. Furthermore, an analysis of the Gibbs free energy uncovers a van der Waals-like first-order phase transition characterized by a distinct swallow-tail structure. We observe a clear physical decoupling in the critical regime: ModMax nonlinearities modify the critical phase boundary by suppressing electromagnetic interactions, Sharma-Mittal parameters dictate the relative thermal stability of competing phases, and massive gravity governs the overarching macroscopic phase landscape. These results highlight the sensitivity of thermodynamic phase phenomena as robust diagnostic tools for distinguishing nonlinear and non-extensive modifications to black hole physics.

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Naba Jyoti Gogoi, Hassan Hassanabadi, Himasri Pinapothu, Dhruba Jyoti Gogoi. 2026-06-24. Extended Thermodynamics and Throttling Process of Charged AdS Black Holes in ModMax-dRGT Massive Gravity with Sharma-Mittal Entropy. https://arxiv.org/abs/2606.26210

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