Probing phase transitions of regular black holes in anti-de Sitter space with Lyapunov exponent

TL;DR

This paper explores how the Lyapunov exponent reflects thermodynamic phase transitions in charged regular anti-de Sitter black holes, revealing oscillatory and discontinuous behaviors near critical points, indicating its potential as an order parameter.

Contribution

It demonstrates the Lyapunov exponent's behavior during phase transitions in black holes, highlighting its role as an indicator and its critical scaling near phase transition points.

Findings

Lyapunov exponent oscillates during phase transitions.

Discontinuous change of Lyapunov exponent at coexistence curve.

Power-law behavior of Lyapunov exponent near critical point with exponent 1/2.

Abstract

We investigate the relationship between thermodynamic phase transitions and the Lyapunov exponent of charged regular anti-de Sitter black holes in quasi-topological gravity. Our results show that the Lyapunov exponent displays oscillatory behavior during phase transitions. Moreover, along the coexistence curve the Lyapunov exponent changes discontinously and continuously at the critical point. Near the critical point, the Lyapunov exponent follows a power-law behavior with a critical exponent of 1/2, suggesting its role as an order parameter and encodes information on black hole phase transitions.