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

TL;DR

This paper develops an approximate axially symmetric solution within a conformal Weyl-Dirac gravitational framework, modeling dark matter as a scalar field, and applies it to explain spiral galaxy rotation curves.

Contribution

It introduces a new conformal Weyl-Dirac gravitational theory with a scalar field for dark matter and derives an approximate solution relevant to galactic rotation.

Findings

Derived a static axially symmetric vacuum solution

Applied the solution to galaxy rotation velocity problems

Provided insights into dark matter effects in galactic dynamics

Abstract

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.