The Stability of Stars with Potential-Dependent Masses

We calculate the effective mass of a spherical star-like object under the assumption that the mass of an object represents a function of the gravitational potential in which it occurs. We show that due to this mass-dependence on the gravitational potential, it is not possible that a star of a larger mass than that of a neutron star shrinks to a point singularity. We present the value of the upper limits to the mass of spherical mass bodies as a function of their radii in a large range of their mass densities.