Scalar Soliton in Newtonian Gravity Modelling Dark Matter Halos

Within standard Newtonian gravity, galactic dark matter is modelled by a scalar field in order to effectively modify Kepler's law. In particular, we show that a solvable toy model with a self-interaction U(Φ) borrowed from non-topological solitons produces already qualitatively correct rotation curves. Although relativistic effects in the halo are very small, we indicate corrections arising from the general relativistic formulation.