Abstract
We present a compact theorem which reveals the fact that static spatially regular massive scalar fields with nonminimal coupling to gravity cannot form spherically symmetric asymptotically flat horizonless matter configurations. In particular, the no-go theorem rules out the existence of boson stars made of static scalar fields with generic values of the physical parameter xi which quantifies the coupling between the spacetime curvature and the massive bosonic fields.
Highlights
The non-linearly coupled Einstein-massive-scalar field equations have a physically interesting and mathematically elegant structure that has attracted the attention of researches during the last five decades
We conclude that static spatially regular massive scalar fields whose nonminimal coupling parameter lies in the dimensionless physical regime ξ ≥ 0 cannot form spherically symmetric asymptotically flat horizonless matter configurations
Boson stars represent self-gravitating horizonless compact objects which are made of massive scalar fields
Summary
The non-linearly coupled Einstein-massive-scalar field equations have a physically interesting and mathematically elegant structure that has attracted the attention of researches during the last five decades (see [1–44] and references therein) This physical system is known to possess asymptotically flat bound-state solutions in the form of rotating hairy black holes that support spatially regular stationary massive scalar field configurations [15–44]. The main goal of the present paper is to reveal the intriguing fact that, as opposed to stationary matter fields, static selfgravitating massive scalar fields with non-minimal coupling to gravity cannot form spatially regular horizonless boundstate matter configurations (boson stars). Below we shall present a remarkably compact no-go theorem for static boson stars which reveals the fact that the non-linearly coupled Einstein-massive-scalar field equations do not admit static spatially regular bound-state solutions made of selfgravitating scalar fields with nonminimal coupling to gravity
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