The Equation of Motion in Rindler Space

The equation of motion of a massive particle in Rindler space or equivalently in an uniform gravitational field has been studied in both classical and quantum mechanical scenarios. The classical geodesics of motion of the particle and the wave function for the quantum mechanical equation satisfied by the particle are obtained. It has been observed that it is equivalent to the problem of free fall of the particle at the center. Unlike the conventional scenario where the fall occurs at the origin, which is a singularity, here it takes place at the point which is at a finite distance from the origin (singularity). Further, the classical trajectories are not a perihelion type. These are closed type. The massive particle returns to its original position if disturbed from the equilibrium position (having minimum energy).

PACS number: 03.65.Ge,03.65.Pm,03.30.+p,04.20.-q.