A Model for Stars of Interacting Bosons and Fermions

TL;DR

This paper models the interactions between bosonic and fermionic matter in compact stars using a current-current interaction term, revealing phase transition behavior similar to BCS theory.

Contribution

It introduces a novel interaction term in gravity coupled to scalar and Fermi fields, analyzing its effects on the system's behavior and phase transitions.

Findings

Different behaviors of scalar field components with increasing interaction

Bose-Fermi system exhibits a BCS-like phase transition

Interaction influences the scalar field dynamics significantly

Abstract

In this paper we introduce a current-current type interaction term in the Lagrangian density of gravity coupled to complex scalar fields, in the presence of a degenerated Fermi gas. For low transferred momenta such a term, which might account for the interaction among boson and fermion constituents of compact stellar objects, is subsequently reduced to a quadratic one in the scalar sector. This procedure enforces the use of a complex radial field counterpart in the equations of motion. The real and the imaginary components of the scalar field exhibit different behaviour as the interaction increases. The results also suggest that the Bose-Fermi system undergoes a BCS-like phase transition for a suitable choice of the coupling constant.