On the universality of Einstein(-Cartan) field equations in the presence of matter fields

Abstract

Within the context of gravity formulated as a gauge theory of the Lorentz group, we derive the field equations for a gravitational action consisting of a generic analytic function of the curvature scalar, in the presence of general matter fields. In the vacuum case we obtain universal equations in agreement with Ferraris et al. We also show explicit non-trivial examples of universal behaviour in the presence of matter fields, which in the general case produces a non-zero torsion field, leading to an Einstein-Cartan geometry and universal Einstein-Cartan field equations.