Approximate axially symmetric solution of the Weyl-Dirac theory of   gravitation and the spiral galactic rotation problem
  On the basis of the Poincare-Weyl gauge theory of gravitation, a new conformal Weyl-Dirac theory of gravitation is proposed, which is a gravitational theory in Cartan-Weyl spacetime with the Dirac scalar field representing the dark matter model. A static approximate axially symmetric solution of the field equations in vacuum is obtained. On the base of this solution in the Newtonian approximation one considers the problem of rotation velocities in spiral components of galaxies. 
O.V. Babourova, B.N. Frolov, P.E. Kudlaev
gr-qc astro-ph.GA