Interplay of Lyapunov exponents, phase transitions and chaos bound in nonlinear electrodynamics black hole

TL;DR

This work analyzes chaos around a four-dimensional nonlinear electrodynamics black hole by computing Lyapunov exponents (LEs) for massless and charged particles via a Jacobian-based approach in equatorial circular orbits. It links these exponents to thermodynamic phase transitions in extended phase space, revealing multivalued LE behavior that tracks the S/L phase coexistence and confirming a mean-field critical exponent $\delta=1/2$ through near-critical expansions. The study also investigates the chaos bound $\lambda \le 2\pi T/\hbar$, showing bound violations occur on the stable small-BH branch and can persist irrespective of phase transitions, with the violation region expanding with angular momentum and charge. Overall, LEs act as a diagnostic tool for black-hole phase structure and chaotic dynamics in nonlinear electrodynamics spacetimes, highlighting a potential link between chaos and thermodynamic stability.

Abstract

In this paper, we investigate Lyapunov exponents of chaos for both massless and charged particles around a non-linear electrodynamics black hole, and explore their relationships with a phase transition and a chaos bound of this black hole. Our results indicate that these exponents can effectively reveal the phase transition. Specifically, during the phase transition, the violation of the chaos bound occurs solely within a stable branch of a small black hole. Moreover, regardless of whether the phase transition takes place, the violations are observed.

Figures (9)

• Figure 1: The variation of the F(r) with respect to the r of the NLED BH
• Figure 2: The critical curve in $Q-\alpha$ parameter space.
• Figure 3: The variation of the temperature with respect to the horizon radius of the NLED BH, where ${\alpha}=0.04$.
• Figure 4: The variation of the Gibbs free energy with respect to the temperature of the NLED BH, where ${\alpha}=0.04$.
• Figure 5: The variation of the LE of chaos for the massless particle with respect to the temperature of the NLED BH.