# Motion of Massive Particles in Rindler Space and the Problem of Fall at the Centre

## TL;DR

This paper explores the classical and quantum behavior of massive particles in Rindler space, revealing unique geodesic paths and a novel fall problem at the sphere's surface, differing from traditional gravitational models.

## Contribution

It provides new insights into particle motion in Rindler space and formulates the quantum fall problem, highlighting differences from Schwarzschild and conventional scenarios.

## Key findings

- Geodesics in Rindler space differ from Schwarzschild case.
- Particles fall at the surface of a sphere, not at the center.
- Quantum analysis shows unique fall behavior in Rindler background.

## Abstract

The motion of a massive particle in Rindler space has been studied and obtained the geodesics of motion. The orbits in Rindler space are found to be quite different from that of Schwarzschild case. The paths are not like the Perihelion Precession type. Further we have set up the non-relativistic Schrodinger equation for the particle in the quantum mechanical scenario in presence of background constant gravitational field and investigated the problem of fall of the particle at the center. This problem is also treated classically. Unlike the conventional scenario, here the fall occurs at the surface of a sphere of unit radius.