This paper investigates the non-Gaussian effects of the Saha equation in Rindler space via Tsallis statistics. By considering a system with cylindrical geometry and the equivalence principle, we deduce the non-Gaussian Saha ionization equation for a partially ionized hydrogen plasma that expands with uniform acceleration. We examine the photoionization of hydrogen atoms and the electron-positron pair production at high temperatures. Our findings reveal that the non-Gaussian binding energy exhibits a quadratic dependence on the gravitational field, in contrast to the linear dependence predicted by Boltzmann-Gibbs statistics. Hence, 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. Finally, constraints on the gravitational field and the electron and positron chemical potentials are derived.

翻译：本文通过Tsallis统计研究林德勒空间中萨哈方程的非高斯效应。通过考虑柱对称几何系统及等效原理，我们推导了均匀加速膨胀的部分电离氢等离子体的非高斯萨哈电离方程。我们研究了高温下氢原子的光电离及电子-正电子对产生过程。结果表明，非高斯结合能对引力场呈二次依赖关系，这与玻尔兹曼-吉布斯统计预言的线性依赖形成对比。因此，在非高斯框架下，强引力场区域中光电离和粒子对产生均比玻尔兹曼-吉布斯框架受到更强抑制。最后，导出了引力场及电子、正电子化学势的约束条件。