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.

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

“…With fieldcurvature couplings, such no hair theorem could also hold in the horizonless gravity [38][39][40]. Moreover, we proved no hair theorem for horizonless compact stars with other boundary conditions [41][42][43].…”

Stationary scalar hairy configurations supported by Neumann compact stars

“…With a nonzero cosmological constant, such no static scalar hair theorem still holds for horizonless neutral reflecting compact stars [30][31][32]. When considering charged horizonless reflecting compact stars, static scalar fields cannot exist outside stars of large size and in contrast, static scalar hair can form outside charged horizonless reflecting compact stars with small radii [33]- [37]. Very differently, if we want to obtain static scalar hair outside asymptotic flat charged black holes, we usually have to put the black hole in a box [38][39][40][41][42][43].…”

No scalar hair theorem for neutral Neumann stars: Static massive scalar fields nonminimally coupled to gravity

“…Large charged reflecting stars also cannot support static scalar field hairs [37][38][39][40][41][42][43][44]. Moreover, it was found that scalar fields cannot exist outside compact stars with Neumann surface boundary conditions [45,46].…”