  We investigate the non-Gaussian effects of the Saha equation in Rindler space
via Tsallis statistics. By considering a system with cylindrical geometry, we
deduce the non-Gaussian Saha ionization equation for a partially ionized
hydrogen plasma that expands with uniform acceleration. We demonstrate
conditions for the validity of the equivalence principle within the realms of
both Boltzmann-Gibbs and Tsallis statistics. In the non-Gaussian framework, our
findings reveal that the effective binding energy exhibits a quadratic
dependence on the frame acceleration, in contrast to the linear dependence
predicted by Boltzmann-Gibbs statistics. We show that an accelerated observer
shall notice a more pronounced effect on the effective binding energy for $a>0$
and a more attenuated one when $a<0$. We also ascertain that an accelerated
observer will measure values of $q$ smaller than those measured in the rest
frame. Besides, assuming the equivalence principle, we examine the effects of
the gravitational field on the photoionization of hydrogen atoms and pair
production. We show that both photoionization and pair production are more
intensely suppressed in regions with a strong gravitational field in a
non-Gaussian context than in the Boltzmann-Gibbs framework. Lastly, constraints
on the gravitational field and the electron and positron chemical potentials
are derived.
