Thermodynamic characteristics of a Fermi gas with an invariant energy scale and its astrophysical implications

Abstract

We investigate the thermodynamics of a relativistic Fermi gas governed by a modified dispersion relation in the Magueijo Smolin (MS) formulation of Doubly Special Relativity (DSR), characterized by the presence of an invariant ultraviolet energy (deformation) scale. We study the system in two physically distinct regimes: the near degenerate low-temperature limit, and the high-temperature regime. In the low-temperature regime, we derive the thermodynamic quantities using the standard Sommerfeld expansion. In the high-temperature regime, we evaluate all thermodynamic quantities numerically from the exact grand canonical potential and demonstrate that the thermodynamics of the Fermi gas reduces to the standard relativistic ideal gas behavior. We apply the resulting low-temperature equation of state to study compact astrophysical objects, namely, non-rotating white dwarfs and neutron stars. Helium white dwarfs exhibit a strong dependence on the deformation scale, while white dwarfs composed of heavier elements are less affected. For neutron stars, the modified equation of state leads to configurations that are smaller in radius and lower in mass than that is produced by nucleonic equations of state. Our results highlight how modified relativity theories can be probed by studying astrophysical objects.