Large regular reflecting stars have no scalar field hair

Abstract: We investigate the gravity system constructed with static scalar fields coupled to asymptotically flat regular reflecting stars. We consider the matter field's backreaction on the reflecting star. We analytically show that there is an upper bound on the radius of the reflecting star. When the star radius is above the bound, the reflecting star cannot support the existence of scalar field hairs. That means large reflecting stars cannot have scalar field hairs.