A no-go theorem for scalar fields with couplings from Ginzburg-Landau models

TL;DR

This paper extends a no-go theorem to show that static scalar fields coupled to their gradients cannot form spherically symmetric boson stars in asymptotically flat spacetimes, highlighting limitations of such models.

Contribution

It generalizes Hod's no-go theorem by including gradient couplings from Ginzburg-Landau models, proving the non-existence of certain boson star solutions.

Findings

No asymptotically flat spherically symmetric boson stars with coupled static scalar fields.

Gradient couplings do not allow static scalar fields to form stable boson stars.

The result applies for non-negative coupling parameters.

Abstract

Recently Hod proved a no-go theorem that static scalar fields cannot form spherically symmetric boson stars in the asymptotically flat background. On the other side, scalar fields can be coupled to the gradient according to next-to-leading order Ginzburg-Landau models. In the present work, we extend Hod's discussions by considering couplings between static scalar fields and the field gradient. For a non-negative coupling parameter, we show that there is no asymptotically flat spherically symmetric boson stars made of coupled static scalar fields.