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arXiv · 2511.09399

Non-commutative geometry and thermodynamics of the Schwarzschild-AdS black hole

Slimane Zaim·Fatma Zohra Bara·Mohamed Aimen Larbei
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Abstract

We investigate the thermodynamic properties of a Schwarzschild-AdS black hole within the framework of noncommutative geometry. We derive and analyze the black hole's thermodynamic functions, showing that they depend critically on the noncommutativity parameter denoted as {\Theta}, while still satisfying the first law of thermodynamics. Stability analysis reveals that the noncommutative Schwarzschild-AdS black hole undergoes a phase transition at a critical point. Moreover, the thermodynamic behavior closely resembles that of a van der Waals fluid, with the noncommutativity introducing a correction term to the black hole's surface temperature. Our results indicate that the noncommutativity parameter {\Theta} is of the order of the Planck scale and functions as a novel thermodynamic variable within the system.

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Slimane Zaim, Fatma Zohra Bara, Mohamed Aimen Larbei. 2025-11-12. Non-commutative geometry and thermodynamics of the Schwarzschild-AdS black hole. https://arxiv.org/abs/2511.09399

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