Boson Stars in a Theory of Complex Scalar Fields coupled to $U(1)$ Gauge Field and Gravity

TL;DR

This paper investigates boson stars and shells within a complex scalar field theory coupled to a U(1) gauge field and gravity, revealing two types of solutions with distinct charge density profiles and exploring their existence domains.

Contribution

It introduces a new potential form combining parabolic and conical features, analyzing boson star solutions in this context with detailed properties and existence conditions.

Findings

Boson stars exhibit ball-like and shell-like charge densities.

Solutions exist within specific parameter domains.

The study extends previous work with similar solutions in V-shaped potentials.

Abstract

We study boson shells and boson stars in a theory of complex scalar field coupled to the $U(1)$ gauge field $A_{\mu}$ and Einstein gravity with the potential: $V(|\Phi|) := \frac{1}{2} m^{2} \left(|\Phi|+ a \right)^2$. This could be considered either as a theory of massive complex scalar field coupled to electromagnetic field and gravity in a conical potential or as a theory in the presence of a potential which is an overlap of a parabolic and a conical potential. Our theory has a positive cosmological constant $(\Lambda := 4 \pi G m^2 a^2)$. Boson stars are found to come in two types, having either ball-like or shell-like charge density. We have studied the properties of these solutions and have also determined their domains of existence for some specific values of the parameters of the theory. Similar solutions have also been obtained by Kleihaus, Kunz, Laemmerzahl and List, in a V-shaped scalar potential.