Lyapunov exponents and phase transition of charged Ads black hole in quintessence

TL;DR

This paper explores how Lyapunov exponents can be used to analyze phase transitions in charged AdS black holes within a quintessence field, revealing their thermodynamic behavior and critical phenomena.

Contribution

It introduces Lyapunov exponents as a novel dynamical tool to study black hole thermodynamics in the presence of quintessence dark energy.

Findings

Lyapunov exponents decrease with increasing quintessence normalization.

Finite cutoff in Lyapunov exponents distinguishes quintessence black holes.

Discontinuity in Lyapunov exponents acts as an order parameter with critical exponent 1/2.

Abstract

This study investigates the phase transitions of RN-AdS black holes immersed in a quintessence field, employing Lyapunov exponents as a dynamical probe to characterize the thermodynamics of black hole. Incorporating quintessence dark energy into the RN-AdS framework, we find that the Lyapunov exponents for null and timelike geodesics display diminished chaotic behavior with increasing normalization factor of the quintessence field. This feature introduces a finite cutoff to the Lyapunov exponent of unstable circular photon orbits, setting it apart from RN-AdS black hole. At phase transition points, both the free energy and Lyapunov exponents display multivalued branches, reflecting the coexistence of distinct black hole phases. Furthermore, the discontinuity in the Lyapunov exponent can serve as an order parameter with a critical exponent of $1/2$ near the critical point, consistent with the thermodynamic criticality of van der Waals fluids.. These work suggest that Lyapunov exponents provide a framework for probing the thermodynamics of black holes.