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There seems to be some confusion as to what I am asking, so I am editing this for clarity.

I know the universe is not a black hole. But if I could take all of the matter, (seen and unseen including dark matter) and condensed it down until I made a black hole, how big would the Schwarzchild radius be?

I used the online Omni Schwarzschild Radius Calculator and got a Rs of 922,849,991,811,114,802,777,336,648 miles or 156,983,977,244,214.0625 LY which seems WAY too high

I have worked 80+ hours this week so my math may be off but $10^{55}$ grams is $10^{52}$ kg's, right? So is there a way to calculate the Rs of the observable universe? If for nothing else other than S&G? Would it be a straight forward calculation? or does the mass of the universe cause issues due to the size?

Rick
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  • Something makes me nervous about this question... But then, meeting all friends at once in a single point sounds nice... – Volker Siegel Apr 14 '19 at 07:32
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    As explained by the answer to your previous question on this topic, the universe is not a black hole and does not have a Schwarzschild radius. –  Apr 14 '19 at 14:17
  • @BenCrowell - Yes I am aware the universe is not a black hole. I am trying to find the Schwarzchild radius if I compressed all of the matter in the universe down and made a black hole out of it. The calculator I used gave me a nonsensical answer of 156B light years. and I am trying to figure out what went wrong. – Rick Apr 14 '19 at 14:23
  • Rick, this is tangential to your question, but for this type of the back-of-the envelope calculation always use 900,000,000,000,000,000,000,000,000 instead of 922,849,991,811,114,802,777,336,648. One of my profs used to fail students on tests for this, and rightly so. Probably the most precisely measured physical quantity to date is the electron anomaly ${g_e}-2$, and it is known to "only" 12 significant digits. No number with 28 significant digits can be physical. Since you started with one significant digit in $10^{55}$, so you have no more than one in the result. – kkm -still wary of SE promises Apr 14 '19 at 14:56
  • This has been asked and answered here: https://physics.stackexchange.com/q/1901/115253 (But @StephenG answer adds more to the accepted answer there, IMO). – kkm -still wary of SE promises Apr 14 '19 at 15:07

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A Schwarzchild radius refers to a model of a static and eternal (unchanging) idealized model for a gravitational field. The universe is anything but this - it is expanding and the simplest metric to model the universe with is the FLRW metric, and a Schwarzchild radius is pretty meaningless for that model.

You should note in particular that the FLRW metric means that there is no center to the universe. This contrasts with the Schwarzchild metric which explictly models a mass/energy with a definite central position and defines that as it's origin. In FLRW you effectively define the observer as being at the origin. So with a Schwarzchild metric observers can be anywhere relative to the origin, but not in FLRW.

I would say the concepts that are relevant in FLRW are the Cosmological Horizon which are described on this Wikipedia page. The simplest way to describe these is that as the universe expands, the most distant parts are moving (mostly due to the expansion of the universe) away from the observer and there is a "bubble" which has less and less in it as time goes by and it's only from this "bubble" - this small part of the universe - that you can make observations. Everything outside your "bubble" - the bit of the universe you can access - is unobservable, depending on precisely what you mean by that.

But that radius is not constant and changes with time. This again contrasts with a Schwarzchild radius, which is static and unchanging and is eternal.

The mass of the universe is not enough anyway - you need to factor in all energy (energy distorts spacetime, matter is just one form of energy) in the universe, and the bulk of that is not is "common" matter but in Dark Matter and Dark Energy. Which leads to the question what is the total energy of the universe and that is not at all trivial - I suggest reading the answers to Is the total energy of the universe zero?.

StephenG - Help Ukraine
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  • My goal was to try and find out what the Rs was tif I condensed the entire universe down to make a black hole. – Rick Apr 14 '19 at 12:05