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

Understand

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.