Quasi-homogeneous black hole geometrothermodynamics in Einstein-Maxwell theory
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913099069521920 |
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| author | Quevedo, Hernando |
| author_facet | Quevedo, Hernando |
| contents | In this review, we establish the mathematical framework of geometrothermodynamics (GTD) as a formalism capable of describing non-extensive, quasi-homogeneous, self-gravitating systems in a Legendre-invariant manner. We argue that the fundamental equations of black holes are quasi-homogeneous functions, a property that invalidates the standard Euler identity of laboratory thermodynamics. We derive the metrics for the equilibrium manifold and analyze their curvature singularities for the Reissner-Nordström, Kerr, and Kerr-Newman black holes. Furthermore, we establish a direct correspondence between the curvature singularities of the equilibrium space and phase transitions, as determined by the divergences of the corresponding heat capacities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06602 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quasi-homogeneous black hole geometrothermodynamics in Einstein-Maxwell theory Quevedo, Hernando General Relativity and Quantum Cosmology In this review, we establish the mathematical framework of geometrothermodynamics (GTD) as a formalism capable of describing non-extensive, quasi-homogeneous, self-gravitating systems in a Legendre-invariant manner. We argue that the fundamental equations of black holes are quasi-homogeneous functions, a property that invalidates the standard Euler identity of laboratory thermodynamics. We derive the metrics for the equilibrium manifold and analyze their curvature singularities for the Reissner-Nordström, Kerr, and Kerr-Newman black holes. Furthermore, we establish a direct correspondence between the curvature singularities of the equilibrium space and phase transitions, as determined by the divergences of the corresponding heat capacities. |
| title | Quasi-homogeneous black hole geometrothermodynamics in Einstein-Maxwell theory |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2605.06602 |