No nonminimally coupled massless scalar hair for spherically symmetric neutral reflecting stars

TL;DR

This paper proves that spherically symmetric, neutral reflecting stars cannot support static configurations of nonminimally coupled massless scalar fields, extending previous no-hair theorems to include nonminimal coupling.

Contribution

It extends the no-hair theorem to nonminimally coupled scalar fields, showing such fields cannot exist around reflecting stars.

Findings

Nonminimally coupled massless scalar fields cannot form static configurations around reflecting stars.

The no-hair property holds even with nonminimal coupling.

Supports the uniqueness of reflecting star solutions without scalar hair.

Abstract

It has recently been proved that horizonless compact stars with reflecting boundary conditions {\it cannot} support spatially regular matter configurations made of minimally coupled scalar fields, vector fields, and tensor fields. In the present paper we extend this intriguing no-hair property to the physically interesting regime of scalar fields with {\it nonminimal} coupling to gravity. In particular, we prove that static spherically symmetric configurations made of nonminimally coupled massless scalar fields cannot be supported by compact reflecting stars.