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arXiv · 2604.08629

Thermodynamics and phase transitions of $\kappa$-deformed Schwarzschild-AdS black holes

A. Naveena Kumara·Vishnu Rajagopal·Puxun Wu
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Abstract

We investigate the thermodynamics of the Schwarzschild-AdS black hole in the framework of \(\kappa\)-deformed non-commutative geometry by constructing an effective \(\kappa\)-deformed Schwarzschild-AdS metric from the \(\kappa\)-deformed Newtonian potential. In the extended phase space, we derive a modified first law and the corresponding Smarr relation by treating the \(\kappa\)-deformation parameter as an additional thermodynamic variable and identifying its conjugate potential. Our analysis shows that \(\kappa\)-deformation induces critical behaviour and phase transitions in an uncharged Schwarzschild-AdS black hole, with a critical ratio \(P_c v_c/T_c \simeq 0.370\) that is independent of the deformation parameter and close to the Van der Waals value.

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A. Naveena Kumara, Vishnu Rajagopal, Puxun Wu. 2026-04-09. Thermodynamics and phase transitions of $\kappa$-deformed Schwarzschild-AdS black holes. https://doi.org/10.1016/j.physletb.2026.140724

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