Rényi Topology of Charged-flat Black Hole: Hawking-Page and Van-der-Waals Phase Transitions
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| Format: | Preprint |
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2023
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| author | Barzi, F. Moumni, H. El Masmar, K. |
| author_facet | Barzi, F. Moumni, H. El Masmar, K. |
| contents | In this paper, we extend the proposed setup in [1,2] for finding the topological charges associated with the Hawking-Page and Van-der-Waals transition points as well as equilibrium phases to catch the nonextensive nature of the black hole entropy, Rigorously speaking we incorporate the Rényi statistics formalism in off-shell Bragg-Williams free energy landscape to examine topologically the Hawking-Page phase transition related to the uncharged/charged-flat black hole in grand canonical and the Van-der- Waals transition in the canonical ensemble and where a vortex/anti-vortex structure is found. For this purpose, we introduce three mappings, the $ψ$- and $ξ$-mapping, for phase transitions classification and the $η$-mapping for equilibrium phases classification. We found that Hawking-Page and Van-der-Waals phase transitions belong to different topological classes and exhibit an interplay of total charge values hinting to a possible new correspondence. Our topological study provides further substantiation for a possible conjecture positing a correspondence between the thermodynamic characteristics of black holes in asymptotically flat spacetime using Rényi statistics, and those in asymptotically Anti-de-Sitter spacetime employing Gibbs-Boltzmann statistics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_14069 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rényi Topology of Charged-flat Black Hole: Hawking-Page and Van-der-Waals Phase Transitions Barzi, F. Moumni, H. El Masmar, K. High Energy Physics - Theory In this paper, we extend the proposed setup in [1,2] for finding the topological charges associated with the Hawking-Page and Van-der-Waals transition points as well as equilibrium phases to catch the nonextensive nature of the black hole entropy, Rigorously speaking we incorporate the Rényi statistics formalism in off-shell Bragg-Williams free energy landscape to examine topologically the Hawking-Page phase transition related to the uncharged/charged-flat black hole in grand canonical and the Van-der- Waals transition in the canonical ensemble and where a vortex/anti-vortex structure is found. For this purpose, we introduce three mappings, the $ψ$- and $ξ$-mapping, for phase transitions classification and the $η$-mapping for equilibrium phases classification. We found that Hawking-Page and Van-der-Waals phase transitions belong to different topological classes and exhibit an interplay of total charge values hinting to a possible new correspondence. Our topological study provides further substantiation for a possible conjecture positing a correspondence between the thermodynamic characteristics of black holes in asymptotically flat spacetime using Rényi statistics, and those in asymptotically Anti-de-Sitter spacetime employing Gibbs-Boltzmann statistics. |
| title | Rényi Topology of Charged-flat Black Hole: Hawking-Page and Van-der-Waals Phase Transitions |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2309.14069 |