A Proposed Unification of Neutron Stars and Black Holes, with Implications from the Recent Radius Measurement of PSR J0740$+$6620.

Neutron stars and black holes are surprisingly similar objects. I examine the theory behind the maximal mass of neutron stars, and find unjustified the assumption that additional gravitational collapse of neutron stars creates black holes. Instead, I propose that black holes are created whenever the physical radius of a compact object is smaller than the object's Schwarzschild radius. My calculations indicate that this should happen for compact objects of mass larger than about 5.3 M$_{\mathrm{}}$. I propose that the apparent lack of compact objects between slightly larger than 2 M$_{\mathrm{}}$ and about 5 M$_{\mathrm{}}$ occurs because any such objects would be unstable neutron stars that would therefore shed mass. I will also discuss the recent measurements of the radius of the massive pulsar PSR J0740$+$6620, along with the implications of these measurements on my proposed unification.