# Fundamental Cosmology Questions

*Most recent answer: 04/01/2014*

- Eric (age 37)

Urbana, IL USA

Although we've answered all these questions before, it may be useful to have them grouped together here.

The black hole solutions of the General Relativity equations assume that outside the event horizon the mass density is comparatively very low. Obviously in the near-uniform starting conditions, that assumption isn't close to true. So with an entirely different mass distribution than in the black hole picture, the solution of the GR equations is entirely different. You can get a little feel for that from a classical picture. Near a black hole, in the Newtonian approximation, you have a very strong field pointing inward. In contrast, in the middle of a uniform sea of mass the field is zero.

"Next, how can the size of black hole grow?" I'm not sure how that connects with the rest of the questions. Formally, from our outside point of view a black hole can't grow because the in-falling matter takes forever (due to gravitational redshift) to travel the last tiny, tiny bit of distance to the event horizon. In fact, by the same token a black hole can't ever quite form. If you make a more practical definition of a black hole, including everything that in practice won't leave until after some enormous Hawking time, it just grows by things falling in.

We do not know how much energy the universe has. If the universe happens to be finite, in one standard way of accounting, the total energy is zero because negative gravitational energy just cancels the positive energy. If the universe is infinite, the question has no obvious meaning. You can find a more sophisticated discussion of the issue here: http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html.

What I suspect you're really trying to get at there is "how could it start from nothing?". Probably it didn't, but knowing how to connect up our universe with a broader structure requires having some sort of quantum gravity theory to replace the starting singularity that would be there if gravity weren't quantized.

You ask something about "entropy" and about "complexity". Physics has no universal laws about or even an established definition of "complexity", so I'll skip the complexity part. With regard to entropy, there are two somewhat mysterious aspects. The first is how, given that entropy of an isolated system is conserved according to the Liouville theorem, entropy could be increasing everywhere now. The answer to that is that the entropies that we consider when we say that the total entropy increases are local entropies. These must increase as the (negative) entropy of quantum entanglement between remote regions also increases. That raises the second question: why the starting local entropy and quantum entanglement of the universe was so low. I don't think we know the answer.

Mike W.

*(published on 04/01/2014)*

## Follow-Up #1: big bang and black holes

- Randy (age 40)

Knoxville TN USA

I've put this in a thread with an earlier answer. The key is that the black hole solution to the general relativity equations arises for a dense mass surrounded by more or less empty space. The almost uniformly dense mass of the Big Bang gives a completely different solution to the same equations.

Mike W.

*(published on 09/23/2014)*

## Follow-Up #2: big bang and black holes

- Bill (age 46)

Champaign IL

See the thread above.

The black hole solution of the general relativistic equations assumes low mass density outside the horizon. A uniform density gives a completely different solution.

Mike W.

*(published on 07/05/2018)*