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

Instituto de Ciencias Nucleares, Universidad Nacional Auto´noma de M´exico,Circuito Exterior, C.U., A.P. 70-543, M´exico D.F. 04510, M´exico(Dated: January 11, 2014)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, spatiallylocalized, attractive, stable spacetime configuration can be sourced by the coherent excitation of ascalar field with positive definite energy density and no Noether charges. In the weak-field regime theresult also applies for configurations with a repulsive gravitational potential. This extends Derrick’stheorem to the case of a general (non-canonical) scalar field, including the self-gravitational effects.Some possible ways out are briefly discussed.