Universal geometric framework for black hole phase transitions: From multivaluedness to classification
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918385826136064 |
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| author | Zhang, Shi-Hao Li, Zi-Yuan Zhang, Jing-Fei Zhang, Xin |
| author_facet | Zhang, Shi-Hao Li, Zi-Yuan Zhang, Jing-Fei Zhang, Xin |
| contents | Recent studies have revealed synchronized multivalued behavior in thermodynamic, dynamical, and geometric quantities during the black hole first-order phase transition, which enables a diagnosis from different perspectives, yet its fundamental origin has remained poorly understood. By constructing a unified geometric framework integrating real analysis and covering space theory, we reveal the universal mathematical mechanism behind this phenomenon. We prove that this multivaluedness originates from two non-degenerate critical points in the temperature function $T(r_+)$, where $r_+$ is the horizon radius, which fold the parameter space into a three-sheeted covering structure. As a direct application, we propose that a black hole undergoes a first-order phase transition if and only if its $T(r_+)$ curve has two extrema. Accordingly, we establish a classification scheme, denoted $A1$, $A2$, and $B$ for black holes. This scheme offers a complementary perspective to classifications based on global topological invariants. Our work provides a theoretical foundation for diagnosing phase transitions via multivaluedness and establishes a unified geometric perspective on black hole thermodynamics, chaotic dynamics, and spacetime structure during first-order phase transitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16629 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal geometric framework for black hole phase transitions: From multivaluedness to classification Zhang, Shi-Hao Li, Zi-Yuan Zhang, Jing-Fei Zhang, Xin General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics Recent studies have revealed synchronized multivalued behavior in thermodynamic, dynamical, and geometric quantities during the black hole first-order phase transition, which enables a diagnosis from different perspectives, yet its fundamental origin has remained poorly understood. By constructing a unified geometric framework integrating real analysis and covering space theory, we reveal the universal mathematical mechanism behind this phenomenon. We prove that this multivaluedness originates from two non-degenerate critical points in the temperature function $T(r_+)$, where $r_+$ is the horizon radius, which fold the parameter space into a three-sheeted covering structure. As a direct application, we propose that a black hole undergoes a first-order phase transition if and only if its $T(r_+)$ curve has two extrema. Accordingly, we establish a classification scheme, denoted $A1$, $A2$, and $B$ for black holes. This scheme offers a complementary perspective to classifications based on global topological invariants. Our work provides a theoretical foundation for diagnosing phase transitions via multivaluedness and establishes a unified geometric perspective on black hole thermodynamics, chaotic dynamics, and spacetime structure during first-order phase transitions. |
| title | Universal geometric framework for black hole phase transitions: From multivaluedness to classification |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2512.16629 |