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

It has recently been proved that horizonless compact stars with reflecting boundary conditions 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 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.