Minimal Length Effects on Motion of a Particle in Rindler Space
arXiv:2007.07744
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 the chaotic behavior is stronger with the increases of the minimal length effects, which manifests that the maximum Lyapunov characteristic exponents mostly grow, and the KAM curves on Poincaré surfaces of 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, it 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.
arXiv commentv1: 23 pages, 8 figures; v2: 24 pages, 8 figures, references added
References in corpus (34)
- Hilbert Space Representation of the Minimal Length Uncertainty Relation
- Probing Planck-scale physics with quantum optics
- Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations
- Short Distance vs. Long Distance Physics: The Classical Limit of the Minimal Length Uncertainty Relation
- Chaos in Schwarzschild Spacetime : The Motion of a Spinning Particle
- GUP parameter from quantum corrections to the Newtonian potential
- Observable Properties of Orbits in Exact Bumpy Spacetimes
- Universality in Chaos of Particle Motion near Black Hole Horizon
- Minimal Length Uncertainty Relation and gravitational quantum well
- Presence of horizon makes particle motion chaotic
- Minimal Length Uncertainty Relation and the Hydrogen Spectrum
- How to observe a non-Kerr spacetime
- Critical escape velocity for a charged particle moving around a weakly magnetized Schwarzschild black hole
- Chaotic motion of particles in the accelerating and rotating black holes spacetime
- Chaotic shadow of a non-Kerr rotating compact object with quadrupole mass moment
- Free motion around black holes with discs or rings: between integrability and chaos - II
- Chaotic Scattering and Capture of Strings by Black Hole
- Deformed Heisenberg algebra with minimal length and equivalence principle
- Fermion's tunnelling with effects of quantum gravity
- Static Equilibria of Charged Particles Around Charged Black Holes: Chaos Bound and Its Violations
- Growth of resonances and chaos for a spinning test particle in the Schwarzschild background
- Mixmaster chaos
- Chaotic dynamics of strings in charged black hole backgrounds
- Chaos from the ring string in Gauss-Bonnet black hole in space
- Quantum gravity, minimum length and Keplerian orbits
- Chaos of Wilson Loop from String Motion near Black Hole Horizon
- Quantum gravity effects on compact star cores
- Chaotic motion in multi-black hole spacetimes and holographic screens
- The dynamics of a spinning particle in a linear in spin Hamiltonian approximation
- Short distance modification of the quantum virial theorem
- The Classical Limit of Minimal Length Uncertainty Relation:Revisit with the Hamilton-Jacobi Method
- Some Astrophysical Aspects of a Schwarzschild Geometry Equipped with a Minimal Measurable Length
- Membrane Paradigm and Holographic DC Conductivity for Nonlinear Electrodynamics
- The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario