Symmetry breaking in (gravitating) scalar field models describing interacting boson stars and Q-balls

TL;DR

This paper explores symmetry breaking in interacting scalar field models of boson stars and Q-balls, revealing new asymmetric solutions and their stability properties in gravitating and non-gravitating regimes.

Contribution

It introduces a detailed analysis of symmetry breaking in interacting boson star and Q-ball models, including the existence of asymmetric solutions and their stability regimes.

Findings

Existence of symmetric and asymmetric solutions for equal frequencies.

Asymmetric solutions may be unstable and decay to symmetric ones.

Parameter regimes where only asymmetric solutions exist for boson stars.

Abstract

We investigate the properties of interacting Q-balls and boson stars that sit on top of each other in great detail. The model that describes these solutions is essentially a (gravitating) two-scalar field model where both scalar fields are complex. We construct interacting Q-balls or boson stars with arbitrarily small charges but finite mass. We observe that in the interacting case - where the interaction can be either due to the potential or due to gravity - two types of solutions exist for equal frequencies: one for which the two scalar fields are equal, but also one for which the two scalar fields differ. This constitutes a symmetry breaking in the model. While for Q-balls asymmetric solutions have always corresponding symmetric solutions and are thus likely unstable to decay to symmetric solutions with lower energy, there exists a parameter regime for interacting boson stars, where only asymmetric solutions exist. We present the domain of existence for two interacting non-rotating solutions as well as for solutions describing the interaction between rotating and non-rotating Q-balls and boson stars, respectively.