Einstein’s bivector fields today: A groupoids picture

A modern description of Einstein’s theory of bivector fields presented in the 1944 papers, 1 is thoroughly discussed. It is shown that the main ideas in the original papers can be nicely interpreted in terms of groupoids, in particular a groupoid which is canonically associated to any manifold that we call “Einstein’s groupoid”, and a class of homomorphisms between groupoids that describe the solutions of Einstein’s proposed equations of motion of the theory. It is also shown why such theory will contain no nontrivial solutions and a natural way to extend it that would provide a meaningful physical theory is proposed.