Axially Symmetric Solution of the Weyl–Dirac Theory of Gravitation and the Problem of Rotation Curves of Galaxies

Abstract

On the basis of the Poincare´–Weyl gauge theory of gravitation, a new conformal Weyl–Dirac theory of gravitation was proposed, formulated in Cartan–Weyl space-time with the Dirac scalar field representing a model of dark matter. A static approximate axially symmetric solution of the field equations in vacuum is obtained. On the basis of this solution, in the Newtonian approximation we consider the problem of rotation velocities in the spiral components of galaxies.