Chaos from the ring string in Gauss-Bonnet black hole in $AdS_5$ space

TL;DR

This paper investigates how the Gauss-Bonnet parameter influences the transition to chaos in the dynamics of a ring string in AdS black hole backgrounds, revealing a threshold beyond which chaos intensifies.

Contribution

It identifies a critical Gauss-Bonnet parameter value that marks the onset of chaos in ring string dynamics within AdS-Gauss-Bonnet black holes, extending understanding beyond AdS-Schwarzschild cases.

Findings

Chaos increases with the Gauss-Bonnet parameter.

A threshold value of the Gauss-Bonnet parameter separates regular and chaotic behavior.

Fast Lyapunov indicators confirm the transition to chaos.

Abstract

By the Poincare sections, the dynamical behaviors of the ring string in the AdS-Gauss-Bonnet (AdS-GB) black hole are studied. A threshold value of the Gauss-Bonnet (GB) parameter $\lambda$ are found by the numerical method, below which the behavior of this dynamical system is no-chaotic and above which the behavior becomes gradually chaotic. The chaotic behavior becomes stronger with the increases of GB parameter. It is different from the case in the AdS-Schwarzschild black hole, which is weakly chaotic. Furthermore, we confirm our findings by the Fast Lyapunov indicators.