No hair theorem for scalar field models with non-minimal derivative coupling around a reflecting star

Studying scalar field around black holes in the context of the no-hair theorem is an important and interesting subject. We investigate no scalar hair theorem for an asymptotically flat horizon-less neutral compact reflecting star. A reflecting star is an object with a reflecting boundary (instead of the absorbing event horizon) on which the scalar field or its derivative are zero . We consider a non-minimal kinetic coupling model such that in the kinetic part, the scalar field is non-minimally coupled to the Einstein tensor. We show that in contrast to the black hole cases, there is no non-trivial hair in this problem.