  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.
