Black holes at a finite distance: Quasi-local restricted phase space formalism
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| Format: | Preprint |
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2026
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| _version_ | 1866918489217826816 |
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| author | Huang, Bai-Hao Zhao, Liu |
| author_facet | Huang, Bai-Hao Zhao, Liu |
| contents | We extend the restricted phase space formalism for spherically symmetric black hole solutions of Einstein-Maxwell theory to the quasi-local regime, with the static observers located at a finite radial distance. The first law and Euler relation for the RN and RN-AdS black holes are proved to hold, but only with the inclusion of an extra pair of thermodynamic variables, i.e. the pressure and the area of the codimension-2 hypersurface on which the observers reside. For the RN black holes, the quasi-local behavior is analyzed in detail. It turns out that the RN black holes in the quasi-local description behaves significantly different from itself in the asymptotic description, but is extremely similar to the RN-AdS black holes in the asymptotic description, e.g. allowing for isocharge temperature-entropy phase transitions and lack of isovoltage temperature-entropy phase transitions. In the neutral limit, the Hawking-Page-like transitions appear in the quasi-local description which is absent in the asymptotic description. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_07236 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Black holes at a finite distance: Quasi-local restricted phase space formalism Huang, Bai-Hao Zhao, Liu General Relativity and Quantum Cosmology High Energy Physics - Theory We extend the restricted phase space formalism for spherically symmetric black hole solutions of Einstein-Maxwell theory to the quasi-local regime, with the static observers located at a finite radial distance. The first law and Euler relation for the RN and RN-AdS black holes are proved to hold, but only with the inclusion of an extra pair of thermodynamic variables, i.e. the pressure and the area of the codimension-2 hypersurface on which the observers reside. For the RN black holes, the quasi-local behavior is analyzed in detail. It turns out that the RN black holes in the quasi-local description behaves significantly different from itself in the asymptotic description, but is extremely similar to the RN-AdS black holes in the asymptotic description, e.g. allowing for isocharge temperature-entropy phase transitions and lack of isovoltage temperature-entropy phase transitions. In the neutral limit, the Hawking-Page-like transitions appear in the quasi-local description which is absent in the asymptotic description. |
| title | Black holes at a finite distance: Quasi-local restricted phase space formalism |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.07236 |