Probing Phase Structure of Black Holes with Lyapunov Exponents

TL;DR

This paper explores the connection between Lyapunov exponents and black hole phase transitions, demonstrating that Lyapunov exponents can serve as indicators of phase changes and critical behavior in black holes.

Contribution

It introduces a novel approach linking Lyapunov exponents to black hole phase transitions, providing new insights into black hole thermodynamics and stability analysis.

Findings

Lyapunov exponents become multivalued at phase transitions

Branches of Lyapunov exponents correspond to black hole phases

Discontinuous changes in Lyapunov exponents act as order parameters with a 1/2 critical exponent

Abstract

We conjecture that there exists a relationship between Lyapunov exponents and black hole phase transitions. To support our conjecture, Lyapunov exponents of the motion of particles and ring strings are calculated for Reissner-Nordstr\"{o}m-AdS black holes. When a phase transition occurs, the Lyapunov exponents become multivalued, and branches of the Lyapunov exponents coincide with black hole phases. Moreover, the discontinuous change in the Lyapunov exponents can be treated as an order parameter, and has a critical exponent of $1/2$ near the critical point. Our findings reveal that Lyapunov exponents can be an efficient tool to study phase structure of black holes.