Thomas–Fermi theory at the Planck scale: A relativistic approach

Abstract Many quantum gravity theories predict a minimal length of the order of the Planck length. This prescription implies a numberof modifications in the phase space structure that have consequences on any statistical mechanics approach. We have recently introduced (Shababi and Ourabah, 2019) a formulation of the Thomas–Fermi model in consistency with the minimal length prescription. Herein we extend our formulation to include relativistic effects. In this occasion, we present a formulation in an N -dimensional space to shed light on the behavior of the different corrections with space dimensionality, and generalize our formulation to include the effect of a very strong magnetic field. To substantiate our point, we apply our model to the screening process and provide estimations of the Fermi length for star interior.