Quantum gravity effects on statistics and compact star configurations

TL;DR

This paper explores how quantum gravity effects, modeled via the Generalized Uncertainty Principle, influence the thermodynamics, structure, and stability of compact stars, revealing small corrections to classical models and new stability regimes.

Contribution

It introduces quantum gravity corrections to the thermodynamics and structure of compact stars, providing new insights into their stability and physical properties.

Findings

Degenerate pressure and energy are increased at low Fermi energy.

The Chandrasekhar limit receives a small positive correction.

Beyond a critical Fermi energy, star radius becomes smaller than Schwarzschild radius.

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.