Infinite Universe Gedanken Experiment

Somewhat linked to the other Infinite Universe thread in this forum, but I didn’t want to introduce this as a hyjack there.

Assuming an Infinite Non Repeating Universe, with physics identical to our own universes.
Is there a most massive black hole in that Universe?

Here I am also assuming that there exists no theoretical maximum mass for a black hole.

If you find a particularly massive black hole, are you guaranteed to be able to find a bigger one elsewhere in that Universe. If not can you ever show that you have found the most massive Black Hole?

Sorry, this isn’t really a Gedanken Experiment since no thought experiment is included in the OP.

[Wayne Newton voice]

That’s a real Gedanke Shame !

[/Wayne Newton voice]

It’s possible that there is a biggest black hole. It’s possible that there isn’t.

Without some detailed assumptions and calculations, it’s tough to say more than that.

Thanks ultrafilter, if there isn’t a biggest black hole, would that mean that an infinitely big black hole would exist somewhere?

Not necessarily. There’s no biggest natural number, but there’s always a bigger one.

Bippy the Beardless, ultrafilter already mentioned that if there is no biggest black hole, that doesn’t imply there’s an infinitely big black hole. It may be worth pointing out that there may even be a bound on how big the black holes are. In other words, maybe there is no biggest black hole, but at the same time it may also be the case that all black holes have a radius less than one light year.

Kim-chi to you Cabbage, in the OP I was saying that this assumes no maximum mass/size limit for any black hole.

But I was hoping for help on the distinction if any between a mathematical construct involving infinity and an existant infinite Universe.

ultra says that even though there is no biggest black hole, it doesn’t mean that an infinitely large black hole exists, And I have no reason to doubt this.

Is there any way to distinguish the two cases I will now try and explain from observation within an infinite universe.
(using bh for black hole throughout)

Case 1. For any bh of size N units there must exist a bh of size N+1 units. So that there is no maximum bh size.

Case 2. For any bh of size N there exists bigger bh’s but they form a converging series of sizes, such that no bh is ever bigger than N+k.

Case 1: mass goes like 1,2,3,4,5,… tends to infinity

Case 2: mass goes like 1, 1.5, 1.75, 1.875, … tends to 2

The two cases seem pretty distinct to me. I’m not sure what you’re asking.

I think you are confusing numbers with physical objects. There may be theoretical or proactical limits to the size of Black holes. The size of a black hole is dependent on the amount of matter in it. Thus one may have a large black hole of n solar masses which may be larger than any other black hole in you infinite universe but which would not be infinite nor in fact much bigger than any black hole in our universe.

Possible cases:

  1. A largest non-infinite black hole
  2. An infinite black hole
  3. Many equally sized largest black holes
  4. Black holes of sizes approaching a finite limit
  5. Black holes of arbitrarily large size.

My spidey sense says anything but 5 is too special-case to be likely, but I don’t know enough about physics to say with any certainty.

It just occurred to me that you can’t have an infinitely massive black hole and still have anything outside of it. Since the black hole would exert an infinite amount of force on everything in the universe, it would quickly absorb it all.

ultrafilter the force would still be limited by speed c. So for an infinite black hole of finite age y years it would not have effect on anything further than y light years away.

Could an infinite diameter black hole exist within an infinite Universe, and not take up the entire volume of that universe.

For my earlier case 1, and case 2 question. The cases are easily distinguished if you can measure all the black holes in the Universe. If though you can only see a limited area of the Universe can you use the data from all the black holes that you mcan see as to whether case 1 or case 2 is more likely to be true?

The only reason that c is the universal speed limit is because it requires infinite energy to accelerate to it. If you have an infinite black hole, you have infinite energy.

Still the limit is c. A 15 billion year old infinite mass black hole would accelerate everything in a 15 billion light year sphere arround it towards it at speed c. But it would (I believe) have 0 effect outside that radius. That is assuming that gravatational force propegates at the speed of light, which I think is expected through general relativity.

if we accept that mass in the universe is quantized, then it is not accurate to say a universe with no biggest blackhole does not contain a blackhole with infinite mass.

with quantized mass, we have Bippy’s case 1. if our mass units are only finitely divisible, we can’t have an upper limit on the mass of black holes unless it is the mass of the largest black hole.

You can’t say anything about an infinite BH - how do you solve equations when one term is infinity?

You can often solve equations where one term is infinity, you just don’t get very interesting answers.
if b=infinity and c != +/- infinity then a=infinity
if c=infinity and b != +/- infinity then a=0
if c=0 and b>0 then a=infinity
if c=0 and b<0 then a=-infinity

No, that’s all wrong. You can’t ever divide by 0 or infinity.

As far as the analysis goes, it’s all done with limits.

Can you have an infinite, non-repeating Universe?

I would think that in an infinite universe, it would have to repeat on many different scales. Haven’t thought about it so first ‘hunch’ could be wrong.