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.

翻译：我们通过Tsallis统计研究了林德勒空间中萨哈方程的非高斯效应。通过考虑具有柱面几何结构的系统，推导了以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。我们证明了在玻尔兹曼-吉布斯统计和Tsallis统计范畴内等效原理的成立条件。在非高斯框架下，研究结果表明有效结合能表现出与参照系加速度的二次依赖关系，这与玻尔兹曼-吉布斯统计预测的线性依赖形成对比。我们证明加速观测者将注意到当$a>0$时对有效结合能的影响更为显著，而当$a<0$时影响更为减弱。我们还确定加速观测者测量到的$q$值将小于静止参照系中测得的值。此外，基于等效原理假设，我们研究了引力场对氢原子光电离和正负电子对产生的影响。研究表明，在非高斯语境下，光电离和正负电子对产生在强引力场区域受到比玻尔兹曼-吉布斯框架更强烈的抑制。最后推导了引力场及电子与正电子化学势的约束条件。