On a problem of dark matter: A centrally symmetric distribution of a   pseudoscalar field in the general relativity
  A precise solution of the general relativity equations for centrally symmetric distribution of a pseudoscalar field with U(1) symmetry is presented. It is found that energy density of the field is restricted in the symmetry center and falls with radial distance at a much slower rate than in numerical simulations of dark matter haloes. This result can solve the cusp problem for galaxies and the problem of rotation curves for galaxy exteriors. 
I. K. Rozgacheva, A. A. Agapov
physics.gen-ph