Lyapunov exponents and phase transitions of Born-Infeld AdS black holes

Abstract

In this paper, we characterize the phase transitons of Born-Infeld AdS black holes in terms of Lyapunov exponents. We calculate the Lyapunov exponents for timelike geodesics in background metric and photon geodesics in effective metric. It is found that black hole phase transitions can be described by multiple-valued Lyapunov exponents. And its phase diagram can be characterized by Lyapunov exponents and Hawking temperature. Besides, the change of Lyapunov exponents can be considered as order parameter, and exists a critical exponent 1/2 near critical point.