The covariant Tolman-Oppenheimer-Volkoff equations II: The anisotropic case

TL;DR

This paper extends the covariant Tolman-Oppenheimer-Volkoff equations to include anisotropic sources in static, spherically symmetric spacetimes, enabling detailed analysis and generation of diverse interior solutions for relativistic stars.

Contribution

It generalizes the TOV equations to anisotropic cases, introduces generating theorems, and develops a reconstruction algorithm for a wide class of interior star solutions.

Findings

Extended equations for anisotropic relativistic stars.

Derived a class of 'quasi-isotropic' star solutions.

Established a reconstruction algorithm for interior solutions.

Abstract

We generalise the covariant Tolman-Oppenheimer-Volkoff equations proposed in arXiv:1709.02818 [gr-qc] 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 generalisation 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.