Configurational entropy and stability conditions of fermion and boson stars

TL;DR

This paper explores the relationship between configurational entropy and the stability of fermion and boson stars, finding a strong correlation that suggests entropy can be used to assess stability in these gravitational systems.

Contribution

It extends previous studies by analyzing interacting Fermi and boson gases forming compact objects, confirming the correlation between configurational entropy minimization and stability points.

Findings

Configurational entropy correlates strongly with stability points.

The correlation's accuracy slightly depends on interaction strength.

Entropy-based assessment can serve as an alternative stability criterion.

Abstract

In a remarkable study by M. Gleiser and N. Jiang [Phys. Rev. D {\bf 92}, 044046, 2015], the authors demonstrated that the stability regions of neutron stars, within the framework of the simple Fermi gas model, and self-gravitating configurations of complex scalar field (boson stars) with various self couplings, obtained through traditional perturbation methods, correlate with critical points of the configurational entropy with an accuracy of a few percent. Recently, P. Koliogiannis \textit{et al.} [Phys. Rev. D {\bf 107}, 044069 2023] found that while the minimization of the configurational entropy generally anticipates qualitatively the stability point for neutron stars and quark stars, this approach lacks universal validity. In this work, we aim to further elucidate this issue by seeking to reconcile these seemingly contradictory findings. Specifically, we calculate the configurational entropy of bosonic and fermionic systems, described by interacting Fermi and boson gases, respectively, that form compact objects stabilized by gravity. We investigate whether the minimization of configurational entropy coincides with the stability point of the corresponding compact objects. Our results indicate a strong correlation between the stability points predicted by configurational entropy and those obtained through traditional methods, with the accuracy of this correlation showing a slight dependence on the interaction strength. Consequently, the stability of compact objects, composed of components obeying Fermi or boson statistics, can alternatively be assessed using the concept of configurational entropy.