In a recent paper, Hod started a study on no scalar hair theorem for
asymptotically flat spherically symmetric neutral horizonless reflecting
compact stars. In fact, Hod's approach only rules out massive scalar fields. In
the present paper, for massless scalar fields outside neutral horizonless
reflecting compact stars, we provide a rigorous mathematical proof on no hair
theorem. We show that asymptotically flat spherically symmetric neutral
horizonless reflecting compact stars cannot support exterior massless scalar
field hairs.Comment: 7 page
