Thermodynamics and phase transitions of $κ$-deformed Schwarzschild-AdS black holes
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| Format: | Preprint |
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2026
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| _version_ | 1866910118180814848 |
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| author | Kumara, A. Naveena Rajagopal, Vishnu Wu, Puxun |
| author_facet | Kumara, A. Naveena Rajagopal, Vishnu Wu, Puxun |
| contents | 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. Interestingly, the \(G - T\) curve exhibits a peculiar double-loop structure, deviating from the standard swallow-tail behaviour associated with a first-order phase transition. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_08629 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Thermodynamics and phase transitions of $κ$-deformed Schwarzschild-AdS black holes Kumara, A. Naveena Rajagopal, Vishnu Wu, Puxun General Relativity and Quantum Cosmology 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. Interestingly, the \(G - T\) curve exhibits a peculiar double-loop structure, deviating from the standard swallow-tail behaviour associated with a first-order phase transition. |
| title | Thermodynamics and phase transitions of $κ$-deformed Schwarzschild-AdS black holes |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2604.08629 |