Non-Gaussian Saha's ionization in Rindler spacetime and the equivalence principle

TL;DR

This paper explores how non-Gaussian statistics influence the Saha ionization equation in Rindler spacetime, revealing effects on binding energy, ionization, and pair production under acceleration and gravity.

Contribution

It derives a non-Gaussian Saha ionization equation in Rindler space and analyzes the impact of acceleration and gravity on ionization and pair production within Tsallis statistics.

Findings

Effective binding energy depends quadratically on acceleration.

Accelerated observers see more pronounced non-Gaussian effects.

Photoionization and pair production are more suppressed in strong gravitational fields.

Abstract

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.