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

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