So we have a consistent picture of evolution from diffuse cloud of atoms to white dwarf. And no white dwarf heavier than 1.4 m is known. The blow up in the mathematics seems to occur in reality as well. There are stars which, overnight or faster, become 20 magnitudes brighter. These are the objects called supernovae.
Physics allows an object about as heavy as the sun to be stable in only a very few sizes.
The first two have been discussed. The third, for nuclear physics reasons, is known as a neutron star. For a clue we return to Kepler's law of areas. That's true for ice skaters, professors in swivel chairs, orbiting planets, and spinning stars. The only one which we can directly check is the sun.