Lyapunov exponents, phase transition and chaos bound in Kerr-Newman AdS spacetime

TL;DR

This paper studies Lyapunov exponents near Kerr-Newman AdS black holes, revealing their role in phase transitions, chaos bounds, and critical phenomena, with violations occurring in small black hole regimes.

Contribution

It demonstrates that Lyapunov exponents effectively probe black hole phase transitions and chaos bounds, with new insights into their critical exponents and violation conditions.

Findings

Lyapunov exponents correlate with phase transitions.

Chaos bound violation occurs in small black holes.

Critical exponents are uniformly 1/2.

Abstract

In this paper, we investigate Lyapunov exponents associated with chaotic motions of both massless and massive particles in the vicinity of a Kerr-Newman AdS black hole. Our exploration focuses on their correlations with the black hole phase transition and the chaos bound. The results demonstrate that these exponents serve as effective probes of the phase transition, with the chaotic Lyapunov exponent of the massless particle offering a more precise characterization. Further calculations indicate that critical exponents linked to these Lyapunov exponents are uniformly 1/2. Notably, the violation of the chaos bound occurs irrespective of whether a phase transition is taking place. Through comparative analysis, we identify a critical radius, and the violation consistently arises when the black hole's radius is less than this critical radius. Moreover, this violation is observed in the spacetime of the stable small black hole during the phase transition.