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In a recent paper, Hod started a study on no scalar hair theorem forasymptotically flat spherically symmetric neutral horizonless reflectingcompact stars. In fact, Hod's approach only rules out massive scalar fields. Inthe present paper, for massless scalar fields outside neutral horizonlessreflecting compact stars, we provide a rigorous mathematical proof on no hairtheorem. We show that asymptotically flat spherically symmetric neutralhorizonless reflecting compact stars cannot support exterior massless scalarfield hairs.

No hair theorem for massless scalar fields outside asymptotically flat horizonless reflecting compact stars