No scalar condensations outside reflecting stars with coupling terms from Ginzburg-Landau models

TL;DR

This paper proves that in asymptotically flat spacetimes, regular reflecting stars cannot support static scalar fields coupled via gradient terms when the coupling parameter is non-negative, extending understanding of scalar field behavior near compact objects.

Contribution

The study demonstrates that scalar fields with gradient couplings cannot form condensations outside reflecting stars under certain conditions, providing new insights into scalar field interactions in curved spacetime.

Findings

No scalar condensations outside reflecting stars with non-negative coupling.

Coupling terms in Ginzburg-Landau models restrict scalar field support.

Results extend no-hair theorems for compact objects.

Abstract

We consider static scalar fields coupled to the gradient where the coupling also appears in next-to-leading order Ginzburg-Landau models. We study condensation behaviors of scalar fields outside regular compact reflecting stars in the asymptotically flat background. For non-negative coupling parameters, we prove that the reflecting star cannot support coupled static scalar fields.