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

Understand

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.