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

TL;DR

This paper studies how Lyapunov exponents relate to phase transitions and chaos bounds in nonlinear electrodynamics black holes, revealing that chaos behavior signals phase changes and violations of chaos bounds occur in stable small black hole branches.

Contribution

It uncovers the connection between Lyapunov exponents, phase transitions, and chaos bounds in nonlinear electrodynamics black holes, highlighting their role as indicators of phase changes.

Findings

Lyapunov exponents can effectively indicate phase transitions.

Violations of the chaos bound occur in stable small black hole branches.

Chaos violations are observed regardless of phase transition presence.

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.