No hair theorem for bound-state massless static scalar fields outside horizonless Neumann compact stars

Abstract

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.

7 pages

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