No scalar hair in nonminimal derivative coupling model for Neumann and Dirichlet reflecting star

TL;DR

This paper proves that scalar fields cannot form hair around reflecting stars when coupled nonminimally to Einstein tensor, under both Dirichlet and Neumann boundary conditions, confirming a no-hair theorem.

Contribution

It extends the no-hair theorem to nonminimal derivative coupling models for reflecting stars with both boundary conditions.

Findings

No scalar hair exists for massless scalar fields.

Conditions for no-hair are specified for massive scalar fields.

The no-hair theorem holds in the studied model.

Abstract

We investigate the existence of scalar hair in the background of a reflecting star. The kinetic part of the scalar field is nonminimally coupled to the Einstein tensor. For both the Dirichlet and the Neumann boundary conditions, we study the no-hair theorem. For the massless case, we show that there is no scalar hair, and in the massive case conditions leading to the no-hair theorem are specified.