Scalar condensation behaviors around regular Neuman reflecting stars

TL;DR

This paper investigates scalar field condensations around regular Neumann reflecting stars, establishing conditions for their existence and the no hair theorem, with bounds on star radii for charged cases.

Contribution

It provides new bounds on the radii of charged reflecting stars supporting scalar condensations, extending understanding of no hair theorems in such backgrounds.

Findings

No hair theorem holds for neutral reflecting stars.

Bounds on star radii determine scalar condensation feasibility.

Scalar configurations exist within specific radius bounds for charged stars.

Abstract

We study static massive scalar field condensations in the regular asymptotically flat reflecting star background. We impose Neumann reflecting surface boundary conditions for the scalar field. We show that the no hair theorem holds in the neutral reflecting star background. For charged reflecting stars, we provide bounds for radii of hairy reflecting stars. Below the lower bound, there is no regular compact reflecting star and a black hole will form. Above the upper bound, the scalar field cannot condense around the reflecting star or no hair theorems exist. And in between the bounds, we obtain scalar configurations supported by Neumann reflecting stars.