# Stationary equilibrium of test particles near charged black branes with the hyperscaling violating factor

## TL;DR

This paper investigates the conditions under which the chaos bound for test particles near charged black branes with hyperscaling violation is violated, revealing dependencies on black brane parameters, temperature, and energy conditions.

## Contribution

It identifies how black brane parameters and energy conditions influence the violation of the chaos bound in particle equilibrium near charged black branes.

## Key findings

- Chaos bound can be violated near extremal black branes.
- Violation likelihood increases when null energy condition is broken.
- Critical parameters for chaos bound violation depend on temperature and energy conditions.

## Abstract

We explore the upper bound of the Lyapunov exponent for test particles that maintain equilibrium in the radial direction near the charged black brane with the hyperscaling violating factor. The influences of black brane parameters (hyperscaling violation exponent $\theta$ and dynamical exponent $z$) are investigated. We show that the equilibrium in the radial direction of test particles can violate the chaos bound. The chaos bound is more easily violated for the near-extremal charged black branes. When the null energy condition ($T_{\mu\nu}\xi^\mu\xi^\nu \geq 0$) is broken, the bound is also more likely to be violated. These results indicate that the chaos bound of particle motion is related to the temperature of the black hole and the null energy condition (NEC). By considering the zero-temperature and $T_{\mu\nu}\xi^\mu\xi^\nu=0$ cases, we obtain the critical parameters $\theta_c$ and $z_c$ for the violation of chaos bound. The chaos bound is always satisfied in the range $\theta > \theta_c$ or $z>z_c$.