  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.
