The effect of the Generalized Uncertainty Principle on the motion of particles near a black hole horizon

Abstract

We study the behaviour of massive particles under different potentials near a static spherical black hole. Our purposes are to apply the Hamilton-Jacobi method for this study and to investigate the effects of a minimal length on the motion of particles in unstable equilibrium near the black hole horizon by deformation of a canonical position-momentum commutation relation. We also obtain the equation of motion for a particle on a path in a plane by considering the special potential corresponding to the cylindrical horizon. We also discuss the behaviour of particles and their energy in terms of the black hole's characteristics with different potentials. For both the standard and deformed cases, we examine the changes in the particle's motion in terms of the potential's coefficients which correspond to the black hole's horizon. (C) 2020 Elsevier B.V. All rights reserved.