Schwartzchild radius and the Big Bang

[saltburnman]

TL;DR Summary

At the Big Bang, it would seem that all matter/energy is within its Schwartzchild radius, so is our universe within an enormous black hole?

From a simple point of view, at the time of the big bang, the full energy/matter of the Universe should surely be within its Schwartzchild radius. Thus the entire Universe is within a huge black hole, and can never escape (i.e. is closed). Is this correct?
What about the period of inflation just after the big bang? Did it come to an end because it reached the Schwartzchild radius?
I can't be the only one to have puzzled at the big bang/black hole paradox, but I have not seen it discussed anywhere. I feel sure that the evolution of spacetime must be involved in a significant way.

 

[PeroK]

Summary:: At the Big Bang, it would seem that all matter/energy is within its Schwartzchild radius, so is our universe within an enormous black hole?

From a simple point of view, at the time of the big bang, the full energy/matter of the Universe should surely be within its Schwartzchild radius. Thus the entire Universe is within a huge black hole, and can never escape (i.e. is closed). Is this correct?
What about the period of inflation just after the big bang? Did it come to an end because it reached the Schwartzchild radius?
I can't be the only one to have puzzled at the big bang/black hole paradox, but I have not seen it discussed anywhere. I feel sure that the evolution of spacetime must be involved in a significant way.

This question gets asked frequently. A black hole forms when a critical mass is confined within the Schwarzschild radius and surrounded by vacuum. The early universe was homogeneous and perhaps infinite and not an isolated mass surrounded by vacuuum. Therefore, it was not a black hole.

 

[saltburnman]

Thank you for your reply, but I'm not sure I fully understand. The homogeneity of matter inside the Schwartzchild radius is irrelevant (to my knowledge) to the existence of a black hole. Or are you saying that the Schwartzchild radius of the universe at the big bang was smaller than the big bang (and throughout all its time evolution)?

 

[PeroK]

Thank you for your reply, but I'm not sure I fully understand. The homogeneity of matter inside the Schwartzchild radius is irrelevant (to my knowledge) to the existence of a black hole. Or are you saying that the Schwartzchild radius of the universe at the big bang was smaller than the big bang (and throughout all its time evolution)?

A black hole, technically, is a vacuum (inside and outside the Schwarzschild radius). The early universe was not a vacuum. If you imagine, falsely, the early universe to be a dense region of matter surrounded by vacuum, then you may wrongly conclude that it could form a black hole.

A large star/mass surrounded by vacuum may collapse into a black hole. The early universe - this is easier to understand if we consider the universe to be infinite - was not surrounded by a vacuum. There is no centre towards which to collapse. Any region would have a homogeneous distribution of matter in all directions.

 

[Ibix]

The point is that black holes form from a dense bit of matter surrounded by vacuum. If it's not surrounded by vacuum but is instead surrounded by more matter of the same density then there's no driver for collapse. There's equal gravitational attraction in every direction, so no "inwards" and "outwards" and no horizon.

Furthermore, matter in the early universe was expanding rapidly, not static or collapsing. That really doesn't look like a black hole.

The general point is that matter just being inside its Schwarzschild radius isn't enough for a black hole to form. It needs to be surrounded by vacuum (or at least much less dense matter) and not undergoing violent expansion.

Edit: incidentally, there's no t in Schwarzschild.

 

[saltburnman]

Thank you PeroK and Ibix. I see now that in the same way that gravity at the centre of the Earth is zero, then a homogeneous universe (with no outside vacuum) will not collapse to a black hole. I've just read elsewhere that the big bang is best described as an explosion in time, rather than mass/energy (so there is no outward flow of mass into empty space; my misconception) which helps me follow your arguments.

 

[PeterDonis]

the entire Universe is within a huge black hole, and can never escape (i.e. is closed). Is this correct?

No. The universe is expanding. For a quantity of matter to form a black hole by the criterion you describe, it needs to be collapsing.

 

[saltburnman]

If a sufficient quantity of matter is within its Schwarzschild radius (with vacuum outside), why does it need to be collapsing? Isn't it by definition already a black hole and anything happening inside the event horizon(/Schwarzschild radius) is unknowable and irrelevant to outside observers.

 

[saltburnman]

After an extensive google search, I find that my musing that the Universe is inside a black hole was described in a Nature article ("The Universe as a Black Hole" Nature 240 (5379): 298–299) by R.K. Pathria (1972)

 

[saltburnman]

Also see:
extract from "The Physics and Relativity FAQ" (just the first specific answer)
Original by Philip Gibbs, 1997. Updated by PEG 1997.Is the Big Bang a black hole?
This question can be made into several more specific questions with different answers.

Why did the universe not collapse and form a black hole at the beginning?
Sometimes people find it hard to understand why the Big Bang is not a black hole. After all, the density of matter in the first fraction of a second was much higher than that found in any star, and dense matter is supposed to curve spacetime strongly. At sufficient density there must be matter contained within a region smaller than the Schwarzschild radius for its mass. Nevertheless, the Big Bang manages to avoid being trapped inside a black hole of its own making and paradoxically the space near the singularity is actually flat rather than curving tightly. How can this be?

The short answer is that the Big Bang gets away with it because it is expanding rapidly near the beginning and the rate of expansion is slowing down. Space can be flat even when spacetime is not. Spacetime's curvature can come from the temporal parts of the spacetime metric which measures the deceleration of the expansion of the universe. So the total curvature of spacetime is related to the density of matter, but there is a contribution to curvature from the expansion as well as from any curvature of space. The Schwarzschild solution of the gravitational equations is static and demonstrates the limits placed on a static spherical body before it must collapse to a black hole. The Schwarzschild limit does not apply to rapidly expanding matter (my emphasis).

 

[PeterDonis]

If a sufficient quantity of matter is within its Schwarzschild radius (with vacuum outside), why does it need to be collapsing? Isn't it by definition already a black hole

No. As the articles you have found by Googling tell you.

 

[PeterDonis]

Isn't it by definition already a black hole

Another way of answering this, and the OP question in this thread, is to note that the definition of "black hole" you are implicitly using is not correct. A black hole is not "a bunch of matter that is inside the Schwarzschild radius for its mass". It is "a region of spacetime that cannot send light signals to infinity".

In the Schwarzschild spacetime geometry, which describes a compact, central massive object surrounded by vacuum, "sending light signals to infinity" means something like "the light signals can get as far away from the central object as you like, if you wait long enough". (The more technical definition is that the light signals end up at future null infinity, and a black hole is a region of spacetime that cannot send light signals to future null infinity.) And it turns out that the surface area of a black hole region of spacetime in this geometry will be $4 \pi r_s^2$, where $r_s$ is the Schwarzschild radius corresponding to the mass of the hole. So it makes sense to think of the hole as confined within a region of "size" equal to the Schwarzschild radius. (Note, however, that the hole is vacuum inside; it is not "made of matter". It's made of spacetime curvature.)

In the expanding FRW spacetime geometry, which describes our universe as a whole, there is no infinity to send light signals to. (The more technical statement is that there is no "future null infinity" in FRW spacetime the way there is in Schwarzschild spacetime; the conformal boundaries of the spacetimes are fundamentally different.) So, strictly speaking, it is impossible to have a black hole at all, according to the technical definition of that term, in FRW spacetime. The best you can do is to have a region of spacetime that, locally, looks like a black hole. And "looks like a black hole" means "is approximated well by a piece of the Schwarzschild spacetime geometry", which means it has to be a compact, central massive object surrounded by vacuum.

In our current universe, there are plenty of objects, like planets, stars, or, if we are willing to accept a coarser level of approximation, even galaxies or groups of galaxies, that can be approximated by a piece of the Schwarzschild spacetime geometry. And of course that set of objects includes the objects that we ordinarily call black holes.

But in the early universe, there were no such objects. There was no region in the early universe that could be approximated even coarsely by the Schwarzschild spacetime geometry. The main reasons for that were that, as has been noted, the early universe was rapidly expanding, and, combined with that, that the early universe was very uniform--there was no gravitational clumping the way there is now. The matter in the early universe was a uniform fluid at very high temperature (and, as noted, expanding rapidly), with no boundary. The Schwarzschild spacetime geometry is simply nothing like that, and cannot describe that.

 

[saltburnman]

PeterDonis, many thanks for your detailed explanation.

 

[PeterDonis]

PeterDonis, many thanks for your detailed explanation.

You're welcome!