The Question
(Submitted April 08, 1997)
If the total mass/energy of Universe was at its beginning
in such a minimum sphere of 10E33 or more, why does it
exist? Such an extraordinary condition and diameter is the
same as it is valid for black holes.
Why does the Universe exist, although its total mass was within
the Schwarzschild radius?
The Answer
This is a very good question, and I will do my best answering it.
In the case of a black hole, the Schwarzschild radius is mathematically
the radius in at which one would have to be moving at the speed of
light in order to escape. Or, the radius that nothing can escape.
This is only a function of the mass  not the density.
Putting the numbers in, the Schwarzschild radius (Rsch) is given by:
Rsch = 3km x Mass; Where the Mass is measured in solar masses.
Now, when do we get a black hole? Answer, when the Schwarzschild
radius is bigger than the object we think might make a black hole.
The Sun (Mass = 1 solar mass) is not a black hole because it is bigger
than 3 km. If we magically shrunk in down to 3km in radius, then it
would become a black hole.
Now back to your question: Why then was the early Universe not a
black hole? Well, lets figure out its Schwarzschild radius to get a
basic rule of thumb idea of what is going on.
Rsch = 3km x Mass of the whole Universe in solar masses
= about 10 to 100 billion light years
= about the current size of the whole Universe
So, in the basic definition of a black hole I used above (where the
size of the object is smaller than the Schwarzschild radius)
the whole Universe is one big black hole with us on the inside.
Therefore, the simple answer is that we are inside the event horizon of
the whole Universe, and there is no way that we can escape the Universe's
grasp.
The more complicated answer is a little different. The Schwarzschild
approximation for a black hole is simply that  an approximation. In
general, the most correct description of gravity everywhere is Albert
Einstein's General Theory of Relativity. This a very mathematically
complicated theory in practice, so we only use it when we have to.
Even then we make many simple assumptions, just so that we can solve the
equations.
When does general relativity become extremely important? Answer, when
the sizes of whatever we are studying become approximately the
Schwarzschild radius. So, general relativity becomes important in
compact objects and it becomes important when we start trying to
understand the Universe as a whole. In the middle, like most things we
deal with, we do not have to worry about it because there are simpler
theories that will give us the same answers.
I hope this helps. Thanks again for your insightful question.
Jonathan Keohane
 for Imagine the Universe!
