Chaotic dynamics of string around charged black brane with hyperscaling violation

TL;DR

This paper investigates the chaotic behavior of closed strings around charged black branes with hyperscaling violation, revealing how temperature, dynamical exponents, and initial conditions influence chaos and string dynamics.

Contribution

It introduces a detailed analysis of how hyperscaling violation and related parameters affect string chaos near black branes, highlighting the role of HV exponent and initial conditions.

Findings

Temperature drives strings to escape or be captured.

HV exponent influences the falling velocity of strings.

Chaotic dynamics are insensitive to winding number.

Abstract

By fast Lyapunov indicator (FLI), we study the chaotic dynamics of closed string around charged black brane with hyperscaling violation (HV). The Hawking temperature, Lifshitz dynamical exponent and HV exponent together affect the chaotic dynamics of this system. The temperature plays the role of driving the closed string to escape to infinity. There is a threshold value $z_{\ast}=2$, below which the string is captured by the black brane no matter where the string is placed at the beginning. However, when $z>2$, the string escapes to infinity if it is placed near the black brane at the beginning, but if the initial position of string is far away from the black brane, it oscillates around the black brane till eternity, which is a quasi-periodic motion. HV exponent plays the role of driving the string falling into the black brane. With the increase of HV exponent $\theta$, the falling velocity becomes faster. We find that when we heat the system with large HV exponent, the chaotic system does not essentially changes. It indicates that the HV exponent plays a very important role in determining the state of the chaotic system. Also we study the the effect from the winding number of the string. The study indicates that the chaotic dynamics of the string is insensitive to the winding number.