I was reading Stephen Hawking's 'The theory of everything' when I came across a very interesting type of universe, the 'zero energy universe' since then, I've read some websites but all they used to prove the hypothesis's authenticity were observations(which was found to be very close to zero, and there would anyways be an unexplained curvature if the energies were not close to zero)
What I am interested in knowing is that in the book, Stephen hawking said, and I am paraphrasing that we can add as much mass as we want to the universe because subsequent negative gravitational potential energy will get added.
Now the boldness with which the line was written, I am convinced that there must be some mathematical proof of this relation between the mass and negative energy being exactly equal to each other, at least in a universe without complications like quantum effects. However, I was not able to find any such proof. Can the universe cook books?