  We study no-hair theorem for horizonless objects, being subject to Neumann
boundary conditions. For massive scalar fields, a no hair theorem for Neumann
compact stars was proved by us in a previous paper, where the nonzero scalar
field mass condition is essential in the proof. In the present work, for
massless scalar fields, we prove a no hair theorem, which claims that
bound-state massless static scalar fields cannot exist outside asymptotically
flat horizonless neutral Neumann compact stars.
