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