# Fermions in the Rindler spacetime

## TL;DR

This paper analyzes the Dirac equation in Rindler spacetime, deriving the energy spectrum and showing how acceleration mimics an external potential, leading to bound states in an accelerated frame.

## Contribution

It provides a novel solution to the Dirac equation in Rindler spacetime and reveals how acceleration influences quantum states, mimicking external potentials.

## Key findings

- Derived a compact expression for the energy spectrum.
- Showed acceleration mimics an external potential.
- Demonstrated formation of bound states due to noninertial effects.

## Abstract

In this paper we study the Dirac equation in the Rindler spacetime. The solution of the wave equation in an accelerated reference frame is obtained. The differential equation associated to this wave equation is mapped into a Sturm-Liouville problem of a Schr\"odinger-like equation. We derive a compact expression for the energy spectrum associated with the Dirac equation in an accelerated reference. It is shown that the noninertial effect of the accelerated reference frame mimics an external potential in the Dirac equation and, moreover, allows the formation of bound states.