  We generalize the Tolman-Oppenheimer-Volkoff equations for space-times
endowed with a Weyssenhoff 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 spin surrounded by vacuum, explore their
properties and discuss how these solutions should be smoothly matched to an
exterior space-time. We study how spin changes the Buchdahl limit for the
maximum compactness of stars. Moreover, under rather generic conditions, we
prove that in the context of a Weyssenhoff like torsion, no static, spherically
symmetric compact objects supported only by the spin can exist. We also provide
some algorithms to generate new solutions.

General Relativity and Quantum Cosmology