Minimal length effects on motion of a particle in Rindler space *

Abstract

Various quantum theories of gravity predict the existence of a minimal measurable length. In this paper, we study effects of the minimal length on the motion of a particle in the Rindler space under a harmonic potential. This toy model captures key features of particle dynamics near a black hole horizon and allows us to make three observations. First, we find that chaotic behavior becomes stronger with increases in minimal length effects, leading predominantly to growth in the maximum Lyapunov characteristic exponents, while the KAM curves on Poincaré surfaces of a section tend to disintegrate into chaotic layers. Second, in the presence of the minimal length effects, it can take a finite amount of Rindler time for a particle to cross the Rindler horizon, which implies a shorter scrambling time of black holes. Finally, the model shows that some Lyapunov characteristic exponents can be greater than the surface gravity of the horizon, violating the recently conjectured universal upper bound. In short, our results reveal that quantum gravity effects may make black holes prone to more chaos and faster scrambling.

Bound on Lyapunov exponent in Einstein-Maxwell-Dilaton-Axion black holes*

“…As elaborated in Ref. [31], this result does not necessarily show that the bound conjectured in Ref. [6] is violated.…”

Report on Chaos Bound Outside Taub-Nut Black Holes

“…In [39], Ge et al believed that this violation was related to the stability of the black holes, and it is possible to solve this violation phenomenon through research on stability. In [42,43], the authors found the violation by exploring the influence of the minimum length effects on the chaotic motion. They believed that this result is not a violation for the conjecture proposed in [31], and the bound can be corrected by the minimum length in the bulk.…”

Angular momentum and chaos bound of charged particles around Einstein–Euler–Heisenberg AdS black holes

“…There are two explanations for the violation of the bound. In [51,52], the authors discussed the minimal length effects on the chaotic motion of the particle, and found that the bound is violated. They believed that the result does not necessarily implies the violation for the bound conjectured in [11], and the bound should be corrected due to the minimal length in bulk.…”