Lyapunov exponents as probes for a phase transition of a Kerr-AdS black hole

TL;DR

This paper investigates how Lyapunov exponents for particles orbiting Kerr-AdS black holes can serve as indicators of phase transitions, revealing that massless particle exponents are particularly effective and identifying a critical exponent value.

Contribution

It introduces the use of Lyapunov exponents as probes for black hole phase transitions and compares their effectiveness for massless and massive particles.

Findings

Lyapunov exponents reflect black hole phase transitions.

Massless particle exponents better indicate phase transitions.

Critical exponent for Lyapunov exponents is 1/2.

Abstract

In this letter, we study proper time Lyapunov exponents and coordinate time Lyapunov exponents of chaos for both massless and massive particles orbiting a four-dimensional Kerr-AdS black hole, and explore their relationships with the phase transition of this black hole. The result reveals that both types of Lyapunov exponents can reflect the occurrence of the phase transition. Specifically, when compared to the proper time and coordinate time Lyapunov exponents of massive particles in chaotic states, the exponents corresponding to massless particles demonstrate a more robust capability in describing the phase transition. Furthermore, we conduct a study on critical exponents associated with these Lyapunov exponents in this black hole, identifying a critical exponent value of 1/2.