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Carloni, Sante; Vernieri, Daniele
Physical review. D, 06/2018, Letnik: 97, Številka: 12Journal Article
We generalize the covariant Tolman-Oppenheimer-Volkoff equations proposed in Carloni and Vernieri Phys. Rev. D 97, 124056 (2018).. 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.
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