# Thomas-Fermi Model in Rindler Space

## TL;DR

This paper explores the behavior of an electron gas modeled by Thomas-Fermi theory within Rindler space, revealing unique periodic and discontinuous electron distributions influenced by uniform acceleration.

## Contribution

It introduces a two-dimensional Thomas-Fermi model in Rindler space and describes novel electron distribution patterns with physical interpretations.

## Key findings

- Electrons form periodic rectangular strip distributions.
- Some regions are void of electrons, others are filled.
- Discontinuous electron distributions are observed in Rindler space.

## Abstract

In this article we have investigated the Thomas-Fermi model for the electron gas in Rindler space. We have found that if the uniform acceleration is along $+x$-direction, then there is $y-z$-symmetry in space. For the sake of mathematical simplicity, we have assumed two dimensional spatial structure ($x-y$) in Rindler space. It has been observed that in two dimensional spatial coordinates the electrons are distributed discontinuously but in a periodic manner in a number of rectangular strips like domain along $\pm y$-direction. Some of them are having void structure, with no electrons inside such rectangular strips, while some are filled with electrons. We call the later type domain as the normal zone. We have also given physical interpretation for such exotic type electron distribution in Rindler space.