In popular science books and articles, I keep running into the claim that the total energy of the Universe is zero, "because the positive energy of matter is cancelled out by the negative energy of the gravitational field".

But I can't find anything concrete to substantiate this claim. As a first check, I did a calculation to compute the gravitational potential energy of a sphere of uniform density of radius R using Newton's Laws and threw in E=mc^2 for energy of the sphere, and it was by no means obvious that the answer is zero !

So, my questions:

1) What is the basis for the claim - does one require General Relativity, or can one get it from Newtonian gravity ?

2) What conditions do you require in the model, in order for this to work ?

3) Could someone please refer me to a good paper about this ?