Approximate axially symmetric solution of the Weyl-Dirac theory of gravitation and the spiral galactic rotation problem

Abstract

On the basis of the Poincaré-Weyl gauge theory of gravitation, a new conformal Weyl-Dirac theory of gravitation is proposed, which is the 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.