Covariant Tolman-Oppenheimer-Volkoff equations. II. The anisotropic case

We generalize the covariant Tolman-Oppenheimer-Volkoff equations proposed in Carloni and Vernieri [Phys. Rev. D 97, 124056 (2018).PRVDAQ0556-282110.1103/PhysRevD.97.124056]. to the case of static and spherically symmetric spacetimes with anisotropic sources. The extended equations allow a detailed analysis of the role of the anisotropic terms in the interior solution of relativistic stars and lead to the generalization of some well-known solutions of this type. We show that, like in the isotropic case, one can define generating theorems for the anisotropic Tolman-Oppenheimer-Volkoff equations. We also find that it is possible to define a reconstruction algorithm able to generate a double infinity of interior solutions. Among these, we derive a class of solutions that can represent "quasi-isotropic" stars.