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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.20919 |
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| _version_ | 1866914288848863232 |
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| author | Bécar, Ramón González, P. A. Moncada, Felipe Vásquez, Yerko |
| author_facet | Bécar, Ramón González, P. A. Moncada, Felipe Vásquez, Yerko |
| contents | We investigate the relationship between dynamical instability and thermodynamic phase transitions in four-dimensional Anti--de Sitter black holes in Einstein gravity coupled to a nonlinear power-law electromagnetic field with exponent $p = 3/4$. In the canonical ensemble, we identify a critical electric charge $Q_c$ separating a regime exhibiting a first-order small/large black-hole (SBH/LBH) phase transition from a regime with a single thermodynamically stable phase. For both massless and massive probes, the thermal profile of the Lyapunov exponent $λ(T)$ becomes multivalued in the SBH/LBH coexistence region and exhibits a finite discontinuity at the transition temperature. This jump vanishes continuously as $Q \to Q_c$, signaling the termination of the first-order transition at a second-order critical point. Near criticality, the Lyapunov discontinuity obeys a universal mean-field scaling law with critical exponent $1/2$. For massless probes, we further analyze the critical impact parameter $b_c$, which displays the same multivalued structure and critical behavior as the Lyapunov exponent. We also demonstrate that the spinodal temperatures, defined by the extrema of the $T(r_h)$ curve where the heat capacity at fixed charge diverges, coincide with singular features in the Lyapunov exponent. Our results identify the Lyapunov exponent as a unified dynamical probe capable of capturing both first-order phase coexistence and second-order critical behavior in black-hole thermodynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20919 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lyapunov Exponents and Phase Transitions in Four-Dimensional AdS Black Holes with a Nonlinear Electrodynamics Source Bécar, Ramón González, P. A. Moncada, Felipe Vásquez, Yerko General Relativity and Quantum Cosmology High Energy Physics - Theory We investigate the relationship between dynamical instability and thermodynamic phase transitions in four-dimensional Anti--de Sitter black holes in Einstein gravity coupled to a nonlinear power-law electromagnetic field with exponent $p = 3/4$. In the canonical ensemble, we identify a critical electric charge $Q_c$ separating a regime exhibiting a first-order small/large black-hole (SBH/LBH) phase transition from a regime with a single thermodynamically stable phase. For both massless and massive probes, the thermal profile of the Lyapunov exponent $λ(T)$ becomes multivalued in the SBH/LBH coexistence region and exhibits a finite discontinuity at the transition temperature. This jump vanishes continuously as $Q \to Q_c$, signaling the termination of the first-order transition at a second-order critical point. Near criticality, the Lyapunov discontinuity obeys a universal mean-field scaling law with critical exponent $1/2$. For massless probes, we further analyze the critical impact parameter $b_c$, which displays the same multivalued structure and critical behavior as the Lyapunov exponent. We also demonstrate that the spinodal temperatures, defined by the extrema of the $T(r_h)$ curve where the heat capacity at fixed charge diverges, coincide with singular features in the Lyapunov exponent. Our results identify the Lyapunov exponent as a unified dynamical probe capable of capturing both first-order phase coexistence and second-order critical behavior in black-hole thermodynamics. |
| title | Lyapunov Exponents and Phase Transitions in Four-Dimensional AdS Black Holes with a Nonlinear Electrodynamics Source |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.20919 |