Metric-Affine Gravity and the Geometric Nature of Matter

We consider the metric-affine geometry whose intrinsic structure is defined in terms of two independent objects: the Riemannian metric and the general affine connection. By means of the metric tensor, for contraction of Riemannain curvature of the affine connection, we form an action density for gravity and matter. Variations of our natural Lagrangian give us two equations. The derived equations contain the Einstein field equation. The other equation describes matter in space-time. In this framework, the affine connection is related to the concept of matter in s*pace-time, so matter can be interpreted as a factor which leads curving and twirling of the space-time manifold.