Generalized First Law and Smarr Formula: Beyond Additivity and Extensivity
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909007451521024 |
|---|---|
| author | Zafar, Usman Bhattacharya, Krishnakanta Bamba, Kazuharu |
| author_facet | Zafar, Usman Bhattacharya, Krishnakanta Bamba, Kazuharu |
| contents | The study of black hole thermodynamics becomes a central topic in gravitational physics, where the first law and the Smarr relation establish a deep connection between spacetime geometry and thermodynamic laws. As we know, these relations depend on the entropy; any modification to the entropy arising from quantum gravity or generalized statistical mechanics may impact the basic thermodynamic framework of black holes. In this work, we develop a general framework for deriving the first law of black hole thermodynamics and the associated Smarr relation for generic spherically symmetric spacetime under a wide class of generalized entropy models. In addition, a generalized Ruppeiner thermodynamic geometry is developed to utilize the generalized entropy model, from which the curvature scalar is determined in a general form. To demonstrate this framework, we assume the Resinser-Nordström black hole and investigate the corresponding extremal and non-extremal phase transition. Interestingly, our analysis reveals that entropy models consistent with the Abè-type composition rule result in a vanishing thermodynamic curvature, whereas violations of this rule exhibit curvature divergences, suggesting a geometric test for the consistency of generalized entropy models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00381 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalized First Law and Smarr Formula: Beyond Additivity and Extensivity Zafar, Usman Bhattacharya, Krishnakanta Bamba, Kazuharu General Relativity and Quantum Cosmology High Energy Physics - Theory The study of black hole thermodynamics becomes a central topic in gravitational physics, where the first law and the Smarr relation establish a deep connection between spacetime geometry and thermodynamic laws. As we know, these relations depend on the entropy; any modification to the entropy arising from quantum gravity or generalized statistical mechanics may impact the basic thermodynamic framework of black holes. In this work, we develop a general framework for deriving the first law of black hole thermodynamics and the associated Smarr relation for generic spherically symmetric spacetime under a wide class of generalized entropy models. In addition, a generalized Ruppeiner thermodynamic geometry is developed to utilize the generalized entropy model, from which the curvature scalar is determined in a general form. To demonstrate this framework, we assume the Resinser-Nordström black hole and investigate the corresponding extremal and non-extremal phase transition. Interestingly, our analysis reveals that entropy models consistent with the Abè-type composition rule result in a vanishing thermodynamic curvature, whereas violations of this rule exhibit curvature divergences, suggesting a geometric test for the consistency of generalized entropy models. |
| title | Generalized First Law and Smarr Formula: Beyond Additivity and Extensivity |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.00381 |