Lyapunov exponents as probes for phase transitions of Kerr-AdS black holes

In this paper, we study proper time and coordinate time Lyapunov exponents of chaos for massless and massive particles, and explore their relationships with phase transitions of four-dimensional and five-dimensional Kerr-AdS black holes. The results reveal that these Lyapunov exponents can reflect the occurrence of phase transitions. Specifically, when compared to the Lyapunov exponents of massive particles in chaotic states, those of massless particles exhibit a more comprehensive ability to describe the phase transitions. Furthermore, we conduct a study on the critical exponents associated with the Lyapunov exponents in four-dimensional Kerr AdS black holes, identifying a critical exponent value of 1/2.
Comment: 23 pages, 10 figures