Abstract
In this paper, we use the Hamilton-Jacobi method to study the behavior of a massive particle under potential due to a black hole and we also introduce the deformed canonical position-momentum commutation relation corresponding to the minimal length to discuss the quantum mechanics based on GUP in an algebraic way. Then we investigate the effects of the minimal length on the motion of a particle perturbed away from an unstable equilibrium near the black hole horizon. In both cases we obtain an equation of motion for a particle traversing a path in a plane in the cylindrical horizon case. We also compare our both analytical results. Beside we discuss the behavior of a particle and its motion path vs. the changes of black hole characteristics under different conditions.
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