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Main Authors: Bécar, Ramón, González, P. A., Moncada, Felipe, Vásquez, Yerko
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2601.20919
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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