Static compact objects in Einstein-Cartan theory

We generalize the Tolman-Oppenheimer-Volkoff equations for space-times endowed with a Weyssenhof-like torsion field in the Einstein-Cartan theory. The new set of structure equations clearly show how the presence of torsion affects the geometry of the space-time. We obtain new exact solutions for compact objects with non-null intrinsic spin surrounded by vacuum, explore their properties, and discuss how these solutions should be smoothly matched to an exterior space-time. We study how the intrinsic spin of matter changes the Buchdahl limit for the maximum compactness of stars. Moreover, under rather generic conditions, we prove that in the context of a Weyssenhof-like torsion, no static, spherically symmetric compact objects supported only by the intrinsic spin can exist. We also provide some algorithms to generate new solutions.