The covariant Tolman-Oppenheimer-Volkoff equations I: The isotropic case

TL;DR

This paper develops a covariant formulation of the TOV equations for isotropic stellar objects, revealing mathematical challenges and providing new solutions and methods for modeling relativistic stars.

Contribution

It introduces a covariant version of the TOV equations, offers new interior solutions, and simplifies the application of generating theorems for relativistic stellar models.

Findings

Identified mathematical issues in solving relativistic stellar interiors.

Derived two new physically relevant solutions.

Simplified the formulation of generating theorems.

Abstract

We construct a covariant version of the Tolman-Oppenheimer-Volkoff equations in the case of isotropic sources. The new equations make evident the mathematical problems in the determination of interior solutions of relativistic stellar objects. Using a reconstruction algorithm we find two physically interesting generalisations of previously known stellar interior solutions. The variables that we use also allow an easier formulation of known generating theorems for solutions associated to relativistic stellar objects.