# On the Eigen Value Problem in Rindler Space

## TL;DR

This paper investigates the eigenvalue problem in Rindler space, revealing real eigenvalues due to PT-symmetry despite a non-Hermitian Hamiltonian, and shows linear quantization of eigen energies influenced by gravitational strength.

## Contribution

It develops an exact formalism for the eigenvalue problem in Rindler space and demonstrates the reality of eigenvalues through PT-symmetry, with classical insights into energy quantization.

## Key findings

- Eigenvalues are real despite non-Hermitian Hamiltonian due to PT-symmetry.
- Eigen energies are linearly quantized.
- System's binding increases with gravitational field strength.

## Abstract

In this article in a very general manner we have investigated the eigen value problem in Rindler space. We have developed the formalism in an exact form. It has been noticed that although the Hamiltonian is non-hermitian, because of the PT-symmetric nature, the eigen values are real, where P and T are the parity operator and the time reversal operator respectively. It has further been observed that the eigen energies are linearly quantized and the binding of the system increases with the increase in the strength of uniform gravitational field although its origin is purely classical.