Polytropic stars in bootstrapped Newtonian gravity

TL;DR

This paper explores self-gravitating polytropic stars within a bootstrapped Newtonian framework, revealing that such stars can surpass traditional compactness limits and are well-described by Gaussian density profiles.

Contribution

It introduces a novel approach to modeling polytropic stars in bootstrapped Newtonian gravity, including solutions with arbitrarily high compactness and Gaussian density approximations.

Findings

Density profiles are well approximated by Gaussians.

No Buchdahl limit is observed, allowing arbitrarily large compactness.

Comparison with GR solutions highlights differences in pressure and density profiles.

Abstract

We study self-gravitating stars in the bootstrapped Newtonian picture for polytropic equations of state. We consider stars that span a wide range of compactness values. Both matter density and pressure are sources of the gravitational potential. Numerical solutions show that the density profiles can be well approximated by Gaussian functions. Later we assume Gaussian density profiles to investigate the interplay between the compactness of the source, the width of the Gaussian density profile and the polytropic index. We also dedicate a section to comparing the pressure and density profiles of the bootstrapped Newtonian stars to the corresponding General Relativistic solutions. We also point out that no Buchdahl limit is found, which means that the pressure can in principle support a star of arbitrarily large compactness. In fact, we find solutions representing polytropic stars with compactness above the Buchdhal limit.