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

TL;DR

This paper proves a no-go theorem showing that static, localized scalar field configurations cannot serve as stable dark matter halos under broad conditions, extending Derrick's theorem to general scalar fields with gravity.

Contribution

It establishes a fundamental no-go result for static scalar field dark matter halos without Noether charges, applicable to general scalar fields and gravitational theories.

Findings

No static, spherically symmetric scalar field halos are possible under specified conditions.

The theorem extends Derrick's no-go result to include gravitational effects and non-canonical scalar fields.

Possible ways to evade the theorem are briefly discussed.

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.