Question about Big Bang and Black Holes

[Mihai]

After the Big Bang it was a short period of inflation. After that the physics that we know is supposed to apply.
After inflation the speed of the expansion was smaller than the speed of light and all the mass of the universe was in a relatively small volume.
Why was not the universe a black hole then ? After all, it has enough mass to create a lot of black holes.
I suppose that the inflation pushed matter (or radiation) beyond the horizon of a black hole with the mass equal to the mass of the universe. Can someone give some numbers and some explanations about that, or at least some pointers to where I can read more about it ?

 

[bcrowell]

After the Big Bang it was a short period of inflation. After that the physics that we know is supposed to apply.
After inflation the speed of the expansion was smaller than the speed of light and all the mass of the universe was in a relatively small volume.

The *present* speed of expansion of the universe is greater than c, in the sense that we can detect light from galaxies that are now and always have been receding from us at more than c: Davis and Lineweaver, Publications of the Astronomical Society of Australia, 21 (2004) 97, msowww.anu.edu.au/~charley/papers/DavisLineweaver04.pdf What you need to realize is that general relativity doesn't really have a useful notion of the relative velocity of distant objects. Therefore velocities like this don't really mean much. They are referred to as coordinate velocities.

Why was not the universe a black hole then ? After all, it has enough mass to create a lot of black holes.

In some ways the big bang singularity is not so different from a time-reversed black-hole singularity. Two big differences are (1) the absence of an event horizon and (2) the fact that simple cosmological solutions are homogeneous and isotropic, whereas black hole solutions have a lower degree of spatial symmetry (rotational symmetry about a point).

I suppose that the inflation pushed matter (or radiation) beyond the horizon of a black hole with the mass equal to the mass of the universe.

The big bang was not an explosion at a certain point in space. It existed everywhere at once. Therefore you can't have a spherical event horizon centered on some special point.

This may be helpful: http://en.wikipedia.org/wiki/Singularity_theorems

 

[Phrak]

The big bang was not an explosion at a certain point in space. It existed everywhere at once. Therefore you can't have a spherical event horizon centered on some special point.

BTW, there is at least one alternative theory that correctly predicts the distribution of cosmic background radiation; the Steinhardt–Turok model as a collision between two branes. In this theory there really is a big bang-like event happening at a single location in spacetime by the collision of two branes in an previously, more or less flat, pre-existent spacetime.

Without taking all the nuts and bolts of this theory too seriously, what they have shown, as was their intent, is that inflation theory should not be taken as confirmed beyond serious dispute even given the latest installment of black body radiation data--if we are to believe the authors.But I meant to ask, if you could answer, as you have found two distinctions already: How would the entropic arrow of time compare between a black hole from an exterior vantage, and a white hole universe, from the interior?

Edit: I should be more concise. We should expect the entropy dS/dt to be greater or equal to zero in any exterior region of a black hole, as anywhere else. dS/d(-R)>=0. In the close-in exterior there is a weak coupling between the inward direction and positive time. By the same token there is a measured coupling between positive time and increased size of the Universe. dS/dR>=0. There seems, naively, to be a difference between the two.

 

[bcrowell]

But I meant to ask, if you could answer, as you have found two distinctions already: How would the entropic arrow of time compare between a black hole from an exterior vantage, and a white hole universe, from the interior?

Edit: I should be more concise. We should expect the entropy dS/dt to be greater or equal to zero in any exterior region of a black hole, as anywhere else. dS/d(-R)>=0. In the close-in exterior there is a weak coupling between the inward direction and positive time. By the same token there is a measured coupling between positive time and increased size of the Universe. dS/dR>=0. There seems, naively, to be a difference between the two.

I don't think the form of a solution to the Einstein field equations has anything to tell us about the entropy of the matter that is present. For example, we could have had a Big Bang in which the entropy of the matter fields was maximal. Instead we had one in which it was much less than maximal.

A much more difficult question is how to count the gravitational degrees of freedom in the determination of entropy. AFAIK this is basically an unsolved problem.

 

[Phrak]

I don't think the form of a solution to the Einstein field equations has anything to tell us about the entropy of the matter that is present. For example, we could have had a Big Bang in which the entropy of the matter fields was maximal. Instead we had one in which it was much less than maximal.

I agree. Maybe we are talking at cross-purposes. The OP asks "Why was not the universe a black hole then?" My answer is that the big bang is a an interior solution of a black hole with stuff falling in, but backwards--so it really falls out.

However, I also note that we don't have any candidates for white holes within the Universe that I know of, and we can call the Universe the interior solution of a white whole so that the Universe and black holes, measured in the same time sense, are entropically reversed.

 

[PeterDonis]

I agree. Maybe we are talking at cross-purposes. The OP asks "Why was not the universe a black hole then?" My answer is that the big bang is a an interior solution of a black hole with stuff falling in, but backwards--so it really falls out.

However, I also note that we don't have any candidates for white holes within the Universe that I know of, and we can call the Universe the interior solution of a white whole so that the Universe and black holes, measured in the same time sense, are entropically reversed.

The current cosmological models are not white hole solutions. White holes, like black holes, are vacuum solutions. The current cosmological models (the FRW solutions) have a nonzero stress-energy tensor so they're not vacuum solutions.

 

[Phrak]

The current cosmological models are not white hole solutions. White holes, like black holes, are vacuum solutions. The current cosmological models (the FRW solutions) have a nonzero stress-energy tensor so they're not vacuum solutions.

Feel free to consider non-ideal black and white holes with dust, if you can.

 

[PeterDonis]

Feel free to consider non-ideal black and white holes with dust, if you can.

Are there any? The whole point is that black and white holes are vacuum solutions. If you mean models like the Oppenheimer-Snyder model, where an "interior" solution describing a collapsing star (a contracting FRW solution) is matched to an "exterior" solution describing a Schwarzschild spacetime, that solution doesn't describe a "black hole" until the collapsing star has fallen below r = 2M and no longer affects the external geometry; the horizon doesn't exist until that has happened. The time reverse of that could, I suppose, be considered a sort of "white hole", whose past horizon disappears when the expanding "dust" reaches r = 2M on its way out. But I don't know if anyone has tried to model the universe with such a solution; my suspicion is that it wouldn't work because it would suffer from an even more acute version of the "horizon problem" that standard FRW models without inflation suffer from, and I don't think an inflationary phase could be used to solve the problem for a "white hole" the way it's used in the standard FRW models. (More precisely, I think trying to add an inflationary phase to a "white hole" model would completely remove the "white hole" portion and the past horizon and make it into the same model as the standard FRW models with inflation.)

 

[Mihai]

First I would like to thank to bcrowell for the link to the Davis and Lineweaver paper - it made me realize that probably I have more misconceptions than I thought.

My original question wanted to be simple - if the universe was located in a small volume in the past (some mention the size of a grapefruit after inflation - see http://www.daviddarling.info/encyclopedia/B/Big_Bang.html (I know that there are probably oversimplifications and debatable issues there, the example is just to make a point not to start a polemic)) and if the universe has such a huge mass, how was the Big Bang successful ?
In my mind a possibility was that gravity started only at moment t=0 and the particles/radiation managed to "outrun" gravity long enough in order to get outside the event horizon of a black hole with the mass of the universe.

Probably the answer is "The big bang was not an explosion at a certain point in space. It existed everywhere at once. Therefore you can't have a spherical event horizon centered on some special point." as given by bcrowell or "that the big bang is a an interior solution of a black hole with stuff falling in, but backwards--so it really falls out." as said by Phrak. My problem with these answers is that I cannot really understand them - they come from the interpretation of a mathematical equation that I do not know and are expressed in terms of a conclusion. In order for me to arrive at the same conclusion I have to do a "jump" which is difficult since the reasoning steps on which the conclusion is based are missing.

Whenever I try to understand the concept of the space expanding I have the problem that I don't understand to which space the "space expanding" refers. It cannot refer to the 4 dimensional space since that is a coordinates space (or a "geometrical" space x,y,z,t) in which only static curves can exist. The expansion of this space would imply the existence of a second time dimension in which this expansion takes place.

If I try to imagine the 3 dimensional space expanding it feels that something is not quite right since it implies that the x, y, z dimensions receive a "special" treatment compared to the t dimension.

So, please, can anyone give a pointer to an explanation ?

 

[bcrowell]

Probably the answer is "The big bang was not an explosion at a certain point in space. It existed everywhere at once. Therefore you can't have a spherical event horizon centered on some special point." as given by bcrowell or "that the big bang is a an interior solution of a black hole with stuff falling in, but backwards--so it really falls out." as said by Phrak. My problem with these answers is that I cannot really understand them - they come from the interpretation of a mathematical equation that I do not know and are expressed in terms of a conclusion. In order for me to arrive at the same conclusion I have to do a "jump" which is difficult since the reasoning steps on which the conclusion is based are missing.

It's good that you don't simply want to take things on faith. A book I always recommend for people starting out with relativity is Relativity Simply Explained, by Gardner. You may find it's too easy, but it's always better to start too easy than too hard.

 

[rover2012]

Hello, I’m new to the site and I wanted to say a couple of things that were on my mind about black holes.
And now my thought on black holes, please give your thoughts.
I have always been a relative thinker ever since I can remember always looking how things work. And then comparing one thing to another.
So as far as black holes are concerned I think if you look at a hurricane on our planet to see what it ultimately is. You will see a swirling mass of matter trying to stabilize itself. Does the matter leave the planet? No. Does it wormhole into another existence? No. It just gathers air to fill in the void until it stabilizes.
Now we are talking gas on planet Earth but if we venture out to a much further and larger scale we can see a spot that is categorized as a black hole. Just like the one in the center of our milky way. Light enters it and it does not return large objects are pulled towards it, and all hope is lost. Nice!
What I Think is happening is that the object in question has gained so much mass that light cannot escape because it has grown so massive.
Not an imaginary suction hole that leads who knows where. But a large spherical object with the greatest mass detected called a black hole.
Which would better be described as a black sphere?
Think of space being full instead of a vacuum. And you might see where this is possible.
Thanks for your time.

The most incomprehensible thing about our universe is that it is comprehensible.
-Albert Einstein

 

[nismaratwork]

Hello, I’m new to the site and I wanted to say a couple of things that were on my mind about black holes.
And now my thought on black holes, please give your thoughts.
I have always been a relative thinker ever since I can remember always looking how things work. And then comparing one thing to another.
So as far as black holes are concerned I think if you look at a hurricane on our planet to see what it ultimately is. You will see a swirling mass of matter trying to stabilize itself. Does the matter leave the planet? No. Does it wormhole into another existence? No. It just gathers air to fill in the void until it stabilizes.
Now we are talking gas on planet Earth but if we venture out to a much further and larger scale we can see a spot that is categorized as a black hole. Just like the one in the center of our milky way. Light enters it and it does not return large objects are pulled towards it, and all hope is lost. Nice!
What I Think is happening is that the object in question has gained so much mass that light cannot escape because it has grown so massive.
Not an imaginary suction hole that leads who knows where. But a large spherical object with the greatest mass detected called a black hole.
Which would better be described as a black sphere?
Think of space being full instead of a vacuum. And you might see where this is possible.
Thanks for your time.

The most incomprehensible thing about our universe is that it is comprehensible.
-Albert Einstein

If I may attempt to decipher this... you're making a case for the "black hole" as something more compact than anything current theory can account for, but that it's still an object and not a region. Your choice of metaphor reveals an unfortunate number of misunderstandings about black holes, especially something as terribly massive as an AGN. A hurricane is mostly a big convection current, which is driven by thermal energy, and releases that energy in the form of kinetic energy (wind, surf, moving). A black hole, even if there is a "nugget" at its center, is still thought to be shrouded behind an event horizon. A black hole requires no fuel, just a set of conditions (mass within a specific radius), and from there it may evaporate over grand timescales. In no way can you move from one concept to the other without doing a disservice to physics AND meteorology.