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Can anyone please explain Hawking-Penrose Singularity Theorems and geodesic incompleteness?

In easy to understand plain English please.

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I'd like to see technical answers too :-) –  Dilaton May 27 '13 at 11:37
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arxiv.org/abs/hep-th/9409195 The first lecture. –  MBN May 27 '13 at 12:01
    
The reference given by MBN is about as readable as you can get. –  twistor59 May 27 '13 at 13:35
    
related: physics.stackexchange.com/q/60869/4552 –  Ben Crowell May 27 '13 at 14:19

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This is something that is difficult to answer easily. However, I wil give you the low-technical answer and hopefully by doing so I dont end up missing something necessary to complete your understanding. In 1988 Hawking published where he and Penrose equations in the case of the universe, space is approximately uniform yet quantifly not. It can be shown that the negative gravitational energy exactly cancels positive energy represented by matter. In other words, the total output energy produced by all the stars in all of the universe is enourmous but equal zero due to the negative absorbtion of space. The implications of this. Since the big bang happenrd 13.72 biklion years ago the universe has been able to expand for that amount of time, therfore it has boundries. There is an estimated amount of total mass in expanding space that can be shown with Einsteins constant for the total distance expanded in 13.72 billion years. Specifically the energy density of the universe is exactly what it should be if it came from an initial state of zero energy. The total amount of energy in the universe equals zero and admittetly within quantum uncertainly. And of course you are aware of the heisenburg uncertainty principle so you can fill in yourself the conclusion. Hopefully i didnt destroy this totally and you find this acceptable.

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Sorry, but this is completely wrong. Every sentence is wrong. –  Ben Crowell Jul 14 '13 at 1:25

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