Affine Dynamics with Torsion

In this study, we give a thorough analysis of a general affine gravity with torsion. After a brief exposition of the affine gravities considered by Eddington and Schr\"{o}dinger, we construct and analyze different affine gravities based on the determinants of the Ricci tensor, the torsion tensor, the Riemann tensor and their combinations. In each case we reduce equations of motion to their simplest forms and give a detailed analysis of their solutions. Our analyses lead to the construction of the affine connection in terms of the curvature and torsion tensors. Our solutions of the dynamical equations show that the curvature tensors at different points are correlated via non-local, exponential rescaling factors determined by the torsion tensor.