# Schwarzschild radius of the Universe

• Ivan Seeking
In summary, the conversation discusses the theory that the universe could be inside a black hole, based on the calculation of the Schwarzschild radius using the equation Rg = 2GM/c2 by German physicist Karl Schwarzschild. However, this theory is not entirely accurate as black hole spacetimes do not resemble FLRW spacetimes. Additionally, there is no consensus on how to define the total energy of the universe, and the concept of a "Schwarzschild radius of the universe" is meaningless. While plugging numbers into equations can sometimes yield surprising results, it is often dismissed as numerology.
Ivan Seeking
Staff Emeritus
Gold Member
We can reliably calculate that radius, the Schwarzschild radius, based on the equation Rg = 2GM/c2 written by German physicist Karl Schwarzschild. And insanely enough, if you gathered all the mass of our universe into a single bundle and plugged it into that equation, you'd get a radius that equals exactly the amount of the universe we can see.
https://www.msn.com/en-us/news/tech...pc=U531&cvid=272cb184de9c48fbbd3b321120e37dac

Michio Kaku has often joked, "If you want to know what it looks like inside of a black hole, look around your room".

But is this true?!?! IF we plug the mass of the known universe into the calculation for the Schwarzschild Radius, we get what is observed? That would be mind-blowing if true!

Last edited:
xAxis
Ivan Seeking said:
IF we plug the mass of the known universe into the calculation for the Schwarzschild Radius, we get what is observed? That would be mind-blowing if true!
It's more or less true in the current epoch, but not exactly so. It'll be true briefly at some point in the future for one instant before it starts becoming less accurate again. It doesn't have anything to do with black holes despite Kaku's implication. Black hole spacetimes don't look much like FLRW spacetimes.

pbuk and Ivan Seeking
Ivan Seeking said:
Michio Kaku has often joked, "If you want to know what it looks like inside of a black hole, look around your room".
I'm pretty sure I hear Carl Sagan (on Cosmos) say, "If you want to know what it looks like inside of a black hole, look around." But I could be misremembering.

Ivan Seeking
gmax137 said:
I'm pretty sure I hear Carl Sagan (on Cosmos) say, "If you want to know what it looks like inside of a black hole, look around." But I could be misremembering.
Well, there isn't much exciting to see in a black hole. Infalling radiation may be blue or red shifted depending on your velocity, but that's about it. The accretion disc will probably be an impressive sight above you, but everywhere else will be pretty much black and unexciting. There's nothing particularly special about the interior of a black hole in GR, until you get to the point where tidal forces rip you apart. Even then l, there's nothing to see particularly, apart from the mess.

vanhees71 and Ivan Seeking
Ibix said:
It's more or less true in the current epoch, but not exactly so. It'll be true briefly at some point in the future for one instant before it starts becoming less accurate again. It doesn't have anything to do with black holes despite Kaku's implication. Black hole spacetimes don't look much like FLRW spacetimes.
Does that include dark matter and dark energy?

Strikes me a bit like the "coincidence" that the physical constants have the values they do, which allows matter to exist.

Ivan Seeking said:
Does that include dark matter and dark energy?
Yes. You can have a simpler model of the universe without dark energy (or does it have to be matter dominated? Not sure without double checking) and then you find that the radius of the observable universe is exactly the Schwarzschild radius. With the mix we have, the radius varies a bit compared to the Schwarzschild radius.
Ivan Seeking said:
Strikes me a bit like the "coincidence" that the physical constants have the values they do, which allows matter to exist.
It isn't much of a coincidence. ##GM/c^2## is a natural length scale for gravitational phenomena when you have mass ##M##, so it's not very surprising that the Schwarzschild radius and the radius of the observable universe are simple multiples of it. That they both happen to be twice it is a bit of a coincidence, but that's about it. Almost any maths you do in GR will spit out the Schwarzschild radius or a simple multiple of it somewhere.

Ivan Seeking
If the expansion is accelerating due to dark energy, then is the sum of all energy in the universe increasing; and therefore the mass of the universe is increasing? I haven't kept up with the thinking on dark energy for a long time now. Or does the dark energy get reduced as the universe expands?

(Time to split this conversation off into a new thread, or do you two want to just get a room?)

phinds, Vanadium 50 and Ivan Seeking
berkeman said:
(Time to split this conversation off into a new thread, or do you two want to just get a room?)
No room! I'm curiously reading that.

fresh_42 said:
No room! I'm curiously reading that.
Well you have the superpowers for el-splitto...

berkeman said:
Well you have the superpowers for el-splitto...
I hope we didn't kill that cat.

berkeman
Ivan Seeking said:
If the expansion is accelerating due to dark energy, then is the sum of all energy in the universe increasing;
There is no consensus on how you even define the total energy of the universe. We only know how to do it in asymptotically flat spacetimes, and cosmological spacetimes aren't asymptotically flat. So, um... maybe?
Ivan Seeking said:
Or does the dark energy get reduced as the universe expands?
Dark energy density remains constant at all times, which means it becomes more important over time as the density of everything else falls. It's tempting to try to equate it to the vacuum energy density of quantum field theory, but the best numbers we can come up with for that differ by about 120 orders of magnitude from the measured value... So we don't really know much about it.

vanhees71 and Ivan Seeking
fresh_42 said:
I hope we didn't kill that cat.
The cat that lays the golden eggs?

Ibix said:
The cat that lays the golden eggs?

We (Germans) basically know this show (~15 min) by heart.

First, if Kaku tells you your mother loves you, check it out.

Second, the "Schwarzschild radius of the universe is meaningless. The universe does not have a Schwarzschild geometry, so it sure doesn't have a Schwarzschild radius. It's like talking about the radius of a cube.

Third, sure, you cal always plug numbers into equations willy-nilly and sometimes get a surprising number pop out. We usuallu call it "numerology" and pay it no mind, although there are people discussing example after example in the BTSM forum/

### ​

timmdeeg, vanhees71, martinbn and 4 others
As we obviously have thread here that is not as serious as others, I dare to ask:

Is it possible that the seed BH we are looking for consisted completely of DM, means: was a result of the collapse of early DM concentrations?

Ivan Seeking
To underscore @Vanadium 50 point, in a BH geomertry, there is singularity in the future of (all world line for Schwarzschild case; some world lines for every BH). In our universe modeled by any plausible FLRW solution vaguely matching observation, there is no singularity in the future of any world line.

An even more basic difference is that the interior of any BH is anisotropic, while isotropy (to a very good approximation) is a fundamental feature of the universe at large scales.

Thus, as in so many other cases, I call total BS on Kaku.

vanhees71, martinbn, Ibix and 2 others
Ibix said:
There is no consensus on how you even define the total energy of the universe. We only know how to do it in asymptotically flat spacetimes, and cosmological spacetimes aren't asymptotically flat. So, um... maybe?

Dark energy density remains constant at all times, which means it becomes more important over time as the density of everything else falls. It's tempting to try to equate it to the vacuum energy density of quantum field theory, but the best numbers we can come up with for that differ by about 120 orders of magnitude from the measured value... So we don't really know much about it.

But if dark energy remains constant, yet the expansion is accelerating, it doesn't seem to require a huge leap of faith to say, the total energy of the universe is increasing. How could that not be true? Where are we losing energy?

Ibix said:
Yes. You can have a simpler model of the universe without dark energy (or does it have to be matter dominated? Not sure without double checking) and then you find that the radius of the observable universe is exactly the Schwarzschild radius. With the mix we have, the radius varies a bit compared to the Schwarzschild radius.

It isn't much of a coincidence. ##GM/c^2## is a natural length scale for gravitational phenomena when you have mass ##M##, so it's not very surprising that the Schwarzschild radius and the radius of the observable universe are simple multiples of it. That they both happen to be twice it is a bit of a coincidence, but that's about it. Almost any maths you do in GR will spit out the Schwarzschild radius or a simple multiple of it somewhere.
That is REALLY going to bother me. LOL! I have a hard time buying the argument this is coincidental. I could believe it is circular reasoning somehow; in fact, I would bet on it! But that it accidently matches, exactly? Hmmm.

I understand Vanadium 50s objections - in principle the S radius should be meaningless in this context - but that it matches "exactly" is still hard to accept. Very strange!

Motore
Ivan Seeking said:
But if dark energy remains constant, yet the expansion is accelerating, it doesn't seem to require a huge leap of faith to say, the total energy of the universe is increasing. How could that not be true? Where are we losing energy?
If one accepts that "dark energy" is really just the cosmological constant, all such nonsense falls into the dustbin where it belongs. (Sigh.)

vanhees71 and Ivan Seeking
Ivan Seeking said:
Michio Kaku has often joked, "If you want to know what it looks like inside of a black hole, look around your room".

But is this true?!?!
No. Michio Kaku is notorious for making claims in pop science contexts that he knows he would never get away with if other physicists were around to challenge them.

vanhees71, Ivan Seeking and phinds
Does it bother you that the sun and the moon's angular diameter matches exact;ly?

Motore, vanhees71 and Ivan Seeking
fresh_42 said:
Is it possible that the seed BH we are looking for consisted completely of DM, means: was a result of the collapse of early DM concentrations?
I don't know that we are looking for a "seed BH". However, it is theoretically possible to have a black hole form from dark matter. It's less probable than with regular matter because it's pretty much collisionless, so doesn't collide, lose energy, slow down, and collapse the way normal matter does. When it could happen is in the early universe when densities were high, but everything is more uniform so finding an overdense region that doesn't contain any normal matter is really improbable. So it's possible to have a black hole that formed from pure dark matter, but the conditions for it to happen are improbable, shading rapidly towards impossible if you mean anything larger than a microscopic black hole.

Ivan Seeking and fresh_42
Ivan Seeking said:
But if dark energy remains constant, yet the expansion is accelerating, it doesn't seem to require a huge leap of faith to say, the total energy of the universe is increasing. How could that not be true? Where are we losing energy?
FLRW spacetimes model the universe as the same everywhere. So the first question is if it's infinite. If it is then its total energy is probably going to be undefined.

The technical details of this are a bit beyond me, so if another contributor tells you I'm wrong they're probably right. As I understand it the problem boils down to understanding how the energy of gravity contributes to the total energy. GR doesn't really do "gravitational potential energy" naturally, but if you don't try to account for it then you can't have an energy conservation law anyway. My understanding is that there's no consensus on how to deal with this. People have come up with solutions, but nowhere near everyone is convinced by them, and the total energy if you do believe them ends up being zero as far as I know.

Ivan Seeking
Ivan Seeking said:
That is REALLY going to bother me. LOL! I have a hard time buying the argument this is coincidental.
Dimensional analysis will tell you that any natural length scale you get out of GR is going to be a dimensionless multiple of ##GM/c^2##. There are no other relevant constants to play with and that's the only mix of ##G##, ##M## and ##c## with a dimension of length. So it's only the 2 that's a coincidence. And it's the same basic equations (Einstein's field equations) in both cases, and spherically symmetric solutions in both cases. So it's not enormously surprising to me that the multiple is the same, although the calculations are for different things and proceed in quite different ways from there.

The other point to note is that you can see out of a black hole. Light falls in and into your retina just fine - it's signalling the other way that's the problem. So the edge of the observable universe (beyond which we cannot see) and a black hole event horizon seen from the inside are very different things.

Ivan Seeking
Does it bother you that the sun and the moon's angular diameter matches exact;ly?
They don't, always.

Ivan Seeking said:
They don't, always.
Neither do the two cosmological calculations you are comparing.

In fact, you can turn the calculation around - assume equality and solve for the age of the universe. Suppose you do this and get 18 Gy (I didn't do the calculation, but that's not a horrific guess). The fact that the universe is only 14 Gy old - would that be a success or a failure?

Ivan Seeking and Motore
Ivan Seeking said:
But if dark energy remains constant, yet the expansion is accelerating, it doesn't seem to require a huge leap of faith to say, the total energy of the universe is increasing. How could that not be true? Where are we losing energy?
Peacock in “Cosmological Physics” calls it an unlimited reservoir of energy, just from my memory, I haven’t the book with me. Constant vacuum energy density and increasing size of the universe means increasing vacuum energy, whereby all other energy densities are decreasing at a known rate.
From that point of view the total energy should be increasing since the universe started to expand accelerated, if I see it correctly.

Ivan Seeking said:
How could that not be true?
Because for it to be true, there would have to be some invariant that corresponds to "the total energy of the universe". And there isn't. The quantity that you intuitively think of as "increasing total energy" because of dark energy is not an invariant; it requires a specific coordinate choice to even be defined.

Ivan Seeking said:
But that it accidently matches, exactly?
Nothing "matches exactly". That's the point. You can wave your hands and find an "M" for the universe that sort of matches, but that "M" is not an invariant any more than the "total energy of the universe" is an invariant. You are dealing with a completely different spacetime geometry from the spacetime geometry of a black hole and the "M" of a black hole has a completely different meaning--in fact a black hole spacetime is vacuum, there is no matter present.

Ivan Seeking
Ivan Seeking said:
This article is not at all reliable. At one point it says the radius of the entire universe (not observable, entire) is 23 trillion light years across, but at another point it says our universe is open, which means it would be spatially infinite. (Our actual best current model says our universe is spatially flat, which is different from both.)

At another point it says that SR says "time stops" at the speed of light, which is a common pop science misstatement.

The article references no actual scientific papers, just other pop science sources.

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