No-go theorem for static scalar field dark matter halos with no Noether charges

Abstract

Classical scalar fields have been considered as a possible effective description of dark matter. We show that, for any metric theory of gravity, no static, spherically symmetric, regular, spatially localized, attractive, stable spacetime configuration can be sourced by the coherent excitation of a scalar field with positive definite energy density and no Noether charges. In the weak-field regime the result also applies for configurations with a repulsive gravitational potential. This extends Derrick's theorem to the case of a general (non-canonical) scalar field, including the self-gravitational effects. Some possible ways out are briefly discussed.

6 pages, no figures. The Appendix A does not appear in the printed version

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• Seeding supermassive black holes with a non-vortical dark-matter subcomponent
• Note on scalars, perfect fluids, constrained field theories, and all that
• Horndeski stars
• No-go theorem for static boson stars
• Boson star superradiance with spinning effects and in time domain
• Unified dark matter: constraints from galaxies and clusters
• Rotation curves and orbits in the scalar field dark matter halo spacetime
• Light rings, gravitational lensing, and ISCOs of exotic compact objects in Einstein-scalar-Maxwell theories