Statistical properties of the one-dimensional Dirac oscillator in Rindler space–time

We study the spin-$1/2$ relativistic fermions influenced by the Dirac oscillator in Rindler's space–time. The energy eigenvalues of this oscillator enable us to calculate the thermodynamic properties of this oscillator by using the Hurwitz zeta function via the Mellin transformation. The effect of the geometry of space–time on these properties is studied.