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

Abstract

We investigate the thermodynamics of the Schwarzschild-AdS black hole in the framework of \(κ\)-deformed non-commutative geometry by constructing an effective \(κ\)-deformed Schwarzschild-AdS metric from the \(κ\)-deformed Newtonian potential. In the extended phase space, we derive a modified first law and the corresponding Smarr relation by treating the \(κ\)-deformation parameter as an additional thermodynamic variable and identifying its conjugate potential. Our analysis shows that \(κ\)-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.

Accepted for publication in Phys. Lett. B

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