  The scalar field endowed with a cosh scalar field potential, behaves exactly
in the same way as cold dark matter (CDM) in the region where the scalar field
oscillates around its minimum. Also, in the linear regime, the scalar field
dark matter (SFDM) hypothesis predicts the same structure formation as the cold
dark matter one. This means that CDM and SFDM are equivalent from the
cosmological point of view. The free parameters of the SFDM model can be fixed
using cosmological observations. In a previous work, we showed by solving the
Einstein Klein Gordon equations, that if we use such parameters, the scalar
field collapses forming stable objects with a mass around $10^{12}M_{\odot}$.
In the present work we use analytical solutions of the flat and weak field
limit of the Einstein- Klein-Gordon equations. With this solutions we show that
its scalar field density profile corresponds to a halo with an almost flat
central density and that this halo coincides with the CDM model in a large
outer region. Such a result could solve the problem of the cusp DM halo in
galaxies without extra hypothesis, adding to the viability of the SFDM model.
Thus, the SFDM model can be seen as an alternative model to the CDM one, with a
self interacting WIMP.
