A new gravitational theory and dark matter problem

Abstract

Abstract We propose a new gravitational theory with torsion based on Riemann–Cartan geometry, in which all physical quantities are dynamical. In addition to the spacetime metric, the gravitational degrees of freedom in this theory also include the torsion and two scalar fields. The energy-momentum tensor of the matter fields in this theory is also proposed. A spherically symmetric static vacuum solution of the theory is obtained. It turns out that this solution can fit the observational data of the rotation curve outside the stellar disk in the Milky Way. Therefore, the galactic dark matter may just be the gravitational effect of the theory with torsion.