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

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.

arXiv comment9 pages, 3 figures, accepted by EPJC

References in corpus (21)

• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• The standard map: From Boltzmann-Gibbs statistics to Tsallis statistics
• Acceleration Radiation for Orbiting Electrons
• Triangle for the entropic index q of non-extensive statistical mechanics observed by Voyager 1 in the distant heliosphere
• Dynamics and Statistics of the Fermi--Pasta--Ulam $\beta$--model with different ranges of particle interactions
• Validity and Failure of the Boltzmann Weight
• Sensitivity to initial conditions of a $d$-dimensional long-range-interacting quartic Fermi-Pasta-Ulam model: Universal scaling
• Equilibrium Temperature for Black Holes with Nonextensive Entropy
• Thermodynamically consistent entropic late-time cosmological acceleration
• The Fermionic Signature Operator and Quantum States in Rindler Space-Time
• Inflation Based on the Tsallis Entropy
• Fermions in the Rindler spacetime
• Classical relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated reference frame
• Systematic analysis of the pp collisions at LHC energies with Tsallis function
• Revisiting noninteracting string partition functions in Rindler space
• Gravitational memory for uniformly accelerated observers
• Role of chemical potential at kinetic freeze-out using Tsallis non-extensive statistics in proton-proton collisions at the Large Hadron Collider
• Non-Gaussian Effects of the Saha's Ionization in the Early Universe
• The Hawking Radiation as Gravitational Fowler-Nordheim Emission in Uniformly Accelerated Frame, in The Non-Relativistic Scenario
• Hydrogen atom wave function and eigen energy in the Rindler space
• Thomas-Fermi Model in Rindler Space