Geometric unification of timelike orbital chaos and phase transitions in black holes
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918398682726400 |
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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 | The deep connection between black hole thermodynamics and spacetime geometry remains a central focus of general relativity. While recent studies have revealed a precise correspondence for null orbits, given by $K = -λ^2$ between the Gaussian curvature $K$ and the Lyapunov exponent $λ$, its validity for timelike orbits had remained unknown. Our work introduces the massive particle surface (MPS) framework and constructs a new geometric quantity $\mathcal{G}$. We demonstrate that $\mathcal{G} \propto -λ^2$ on unstable timelike orbits, thus establishing the geometry-dynamics correspondence for massive particles. Crucially, near the first-order phase transition of a black hole, $\mathcal{G}$ displays synchronized multivalued behavior with the Lyapunov exponent $λ$ and yields a critical exponent $δ=1.0244$. Our results demonstrate that spacetime geometry encodes thermodynamic information, opening a new pathway for studying black hole phase transitions from a geometric perspective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04236 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric unification of timelike orbital chaos and phase transitions in black holes Zhang, Shi-Hao Li, Zi-Yuan Zhang, Jing-Fei Zhang, Xin General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory The deep connection between black hole thermodynamics and spacetime geometry remains a central focus of general relativity. While recent studies have revealed a precise correspondence for null orbits, given by $K = -λ^2$ between the Gaussian curvature $K$ and the Lyapunov exponent $λ$, its validity for timelike orbits had remained unknown. Our work introduces the massive particle surface (MPS) framework and constructs a new geometric quantity $\mathcal{G}$. We demonstrate that $\mathcal{G} \propto -λ^2$ on unstable timelike orbits, thus establishing the geometry-dynamics correspondence for massive particles. Crucially, near the first-order phase transition of a black hole, $\mathcal{G}$ displays synchronized multivalued behavior with the Lyapunov exponent $λ$ and yields a critical exponent $δ=1.0244$. Our results demonstrate that spacetime geometry encodes thermodynamic information, opening a new pathway for studying black hole phase transitions from a geometric perspective. |
| title | Geometric unification of timelike orbital chaos and phase transitions in black holes |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2511.04236 |