Quantum gravity effects on statistics and compact star configurations

Abstract

The thermodynamics of classical and quantum ideal gases based on the Generalized uncertainty principle (GUP) are investigated. At low temperatures, we calculate corrections to the energy and entropy. The equations of state receive small modifications. We study a system comprised of a zero temperature ultra-relativistic Fermi gas. It turns out that at low Fermi energy $\varepsilon_F$, the degenerate pressure and energy are lifted. The Chandrasekhar limit receives a small positive correction. We discuss the applications on configurations of compact stars. As $\varepsilon_F$ increases, the radius, total number of fermions and mass first reach their nonvanishing minima and then diverge. Beyond a critical Fermi energy, the radius of a compact star becomes smaller than the Schwarzschild one. The stability of the configurations is also addressed. We find that beyond another critical value of the Fermi energy, the configurations are stable. At large radius, the increment of the degenerate pressure is accelerated at a rate proportional to the radius.