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 $E=m{c}^2$ 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 ?