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In an episode of Discovery's Curiosity with host Stephen Hawking, he claims the Big Bang event can be explained from physics alone, and does not require the intervention of a creator.

1) His argument is based on that, in the beginning, the universe is an equivalent of a black hole behaving as a quantum mechanical particle that can simply "appear" like a Helium particle in alpha radiation. For a large gravitational field like the black hole in question, time did not exist, and therefore there could not exist a being to create the Big-Bang, since time did not exist.

2) During the Big-Bang, positive energy appeared and negative energy was stored in space, and the net energy created is zero and therefore nothing was created.

I am curious on the foundations of Hawking´s claims in the episode.

Is the Big-Bang black hole really modeled as a quantum mechanical particle? Was there really a black-hole at all? What is the resulting entropy change of this black-hole during an event such as the Big-Bang? Are his claims of negative energy stored in space sound or well accepted?

l3win
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It's not standard gravitational potential energy that cancels out the positive energy of matter, this can be confirmed fairly easily by e.g. considering a two-mass system in freefall.

It's rather just a vacuous (and useless, since it defeats the point of defining energy) definition of $-G_{\mu\nu}/8\pi$ as a sort of "negative gravitational energy" which cancels out $G_{\mu\nu}$. This is pointless, and is not the right answer to the question "How did the big bang create stuff?".

See also https://physics.stackexchange.com/a/2844.