Polymer quantum effects on compact stars models

TL;DR

This paper investigates how polymer quantum effects influence the properties of compact stars, specifically white dwarfs, revealing corrections to their mass and setting bounds on the polymer length scale.

Contribution

It introduces a semiclassical model of degenerate fermion gases in polymer quantum mechanics and applies it to compact star models, deriving bounds on the polymer length scale.

Findings

Polymer corrections modify the mass of compact stars.

A bound on the polymer length scale is established as λ² ≲ 10⁻²⁶ m².

Fermi energy remains unchanged under polymer quantization.

Abstract

In this work we study a completely degenerated fermion gas at zero temperature within a semiclassical approximation for the Hamiltonian arising in polymer quantum mechanics. Polymer quantum systems are quantum mechanical models quantized in a similar way as in loop quantum gravity that allow the study of the discreteness of space and other features of the loop quantization in a simplified way. We obtain the polymer modified thermodynamical properties noticing that the corresponding Fermi energy is exactly the same as if one directly polymerizes the momentum $p_F$. We also obtain the corresponding expansion of thermodynamical variables for small values of the polymer length scale $\lambda$. With this results we study a simple model of a compact object where the gravitational collapse is supported by electron degeneracy pressure. We find polymer corrections to the mass of the star. When compared with typical measurements of the mass of white dwarfs we obtain a bound on the polymer length of $\lambda^2\lesssim 10^{-26}m^2$.