Correspondence between mass/radius of both the observable universe and black holes

[MarkE]

"The mass and radius of the observable universe fit the same relationship defined by the mass and Schwarzschild radius of a black hole". 
I've read this sentence in the book 'Einstein's Monsters: The Life and Times of Black Holes'.

Here's the calculation.

What's the significance of this correspondence? Is it expected that there should be relationship between the two, and if so, why? 

Edited May 12, 2021 by MarkE

[beecee]

47 minutes ago, MarkE said:

"The mass and radius of the observable universe fit the same relationship defined by the mass and Schwarzschild radius of a black hole". 
I've read this sentence in the book 'Einstein's Monsters: The Life and Times of Black Holes'.

Here's the calculation.

What's the significance of this correspondence? Is it expected that there should be relationship between the two, and if so, why? 

I'm puzzled on a few counts by what I see as errors....first from your link "and every galaxy harbors a supermassive black hole at its center"...I'm not sure if that statement is really concrete as your article says... https://www.forbes.com/sites/brucedorminey/2020/12/20/galaxy-may-be-missing-its-supermassive-black-hole-says-nasa/?sh=7d361d59735b perhaps its hard to detect because its dormant? Yes certainly most spiral galaxies as well as others do have SMBH's at their core........

 

The other point gets to the title of your thread, re the mass/radius of the observable universe and BH's. Your link gives the radius of the observable universe as 14 billion light years. That refers to how long ago the BB occured...13.83 billion years ago. Due to spacetime expansion the radius of the observable universe is about 47 billion light years.

Plus the observable univere's parameters are determined by how much the universe has expanded, the rate/decelleration/acceleration and the speed of light. In other words, anything beyond how far any light could travel within the age of the universe [13.83 billion years] is beyond the observable universe. This is about 14 parsecs or 47 billion light years radius.

Edited May 12, 2021 by beecee

[MarkE]

@beecee So both the author of the book, as well as this calculation, are wrong?

Edited May 12, 2021 by MarkE

[swansont]

The calculation looks fine. It's the radius of the observable universe that's wrong.

[MarkE]

53 minutes ago, swansont said:

The calculation looks fine. It's the radius of the observable universe that's wrong.

So there is no correspondence between the Schwarzschild radius of a black hole and the observable universe (as these two sources both are wrongfully implying)?

[swansont]

17 minutes ago, MarkE said:

So there is no correspondence between the Schwarzschild radius of a black hole and the observable universe (as these two sources both are wrongfully implying)?

No, they're different by a factor of about 3

An interesting question might be whether they had similar values at some time in the past. With less expansion I would expect the difference between (age)*(speed of light) and R_s is smaller.

[beecee]

 

23 minutes ago, beecee said:

I'm puzzled on a few counts by what I see as errors....first from your link "and every galaxy harbors a supermassive black hole at its center"...I'm not sure if that statement is really concrete as your article says... https://www.forbes.com/sites/brucedorminey/2020/12/20/galaxy-may-be-missing-its-supermassive-black-hole-says-nasa/?sh=7d361d59735b perhaps its hard to detect because its dormant? Yes certainly most spiral galaxies as well as others do have SMBH's at their core........

 

The other point gets to the title of your thread, re the mass/radius of the observable universe and BH's. Your link gives the radius of the observable universe as 14 billion light years. That refers to how long ago the BB occured...13.83 billion years ago. Due to spacetime expansion the radius of the observable universe is about 47 billion light years.

Plus the observable univere's parameters are determined by how much the universe has expanded, the rate/decelleration/acceleration and the speed of light. In other words, anything beyond how far any light could travel within the age of the universe [13.83 billion years] is beyond the observable universe. This is about 47 billion light years radius.

Obviously the highlighted bit by me  is wrong. 14 parsecs = 45.6  light years

and

14x 10 to the 9th power =  4,660,000,000

sorry for the stuffup. Like I said, I'll leave the maths to swansont.

Underlying correction also to my first post....scrub the "14 parsecs or"

Edited May 12, 2021 by beecee

[joigus]

1 hour ago, swansont said:

No, they're different by a factor of about 3

An interesting question might be whether they had similar values at some time in the past. With less expansion I would expect the difference between (age)*(speed of light) and R_s is smaller.

Good point. I think before the universe was vacuum-dominated, the calculation with just energy density of matter and radiation works quite well, and you can actually do the calculation by Newton's gravitation, the result giving coincidence between Schwarzschild's radius and radius of observable universe. I suppose you could do the trick of including an additional term to the total content of the energy by adding vacuum energy, then you would have to recalculate Schwarzschild's radius and everything would check again.

[MarkE]

On 5/12/2021 at 3:14 PM, joigus said:

Good point. I think before the universe was vacuum-dominated, the calculation with just energy density of matter and radiation works quite well, and you can actually do the calculation by Newton's gravitation, the result giving coincidence between Schwarzschild's radius and radius of observable universe. I suppose you could do the trick of including an additional term to the total content of the energy by adding vacuum energy, then you would have to recalculate Schwarzschild's radius and everything would check again.

So there is a correspondence? Could you elaborate some more please, I'm trying to understand what the difference between your statement/calculation and the non-correspondence is (al already pointed out by @swansont). I already thought that it would be unlikely that those two sources that I shared in my initial questions would both, independently, claim the exact same thing, but would both be wrong. @beecee pointed out that they probably meant something else as the way I was interpreting it, and your comment seems to show what this is, so I believe you're on the right track in better explaining what they meant by it. Could you therefore please elaborate a bit more on this? 

Edited May 18, 2021 by MarkE

[joigus]

44 minutes ago, MarkE said:

So there is a correspondence? Could you elaborate some more please, I'm trying to understand what the difference between your statement/calculation and the non-correspondence is (al already pointed out by @swansont). I already thought that it would be unlikely that those two sources that I shared in my initial questions would both, independently, claim the exact same thing, but would both be wrong. @beecee pointed out that they probably meant something else as the way I was interpreting it, and your comment seems to show what this is, so I believe you're on the right track in better explaining what they meant by it. Could you therefore please elaborate a bit more on this? 

There is a correspondence, but it's nothing very deep, I must warn you. GR is very ambiguous as to what is energy in the sense that there are different energy "components" and all can even be arranged to add up to zero. You can call the Einstein field tensor "geometric energy-momentum tensor" if you wish... 

Because the Schwarzschild radius depends on what kind of energy you consider as contained within your volume, you can add up all the terms (matter, radiation, dark matter, and vacuum energy) and your recalculated radius would coincide with the radius of the observable universe. Any horizon is characterised by the receding velocity being v=c, so it's more a dimensional question than anything else. Now, physicists do distinguish vacuum energy from all the rest because conceptually it's very different, thereby the mismatch. I hope that was helpful/clear. Maybe later I have more time to elaborate further.

Dark energy is everywhere, and is constant. The value of the density is very low, but it fills even the largest intergalactic voids, so it contributes a lot in terms of cosmic parameters, very significantly affecting the receding velocity when you reach the cosmic horizon. In fact, it is thought to be the dominant effect at this point in the history of the universe.