How does the expansion of the Universe affect black holes?

[Yashraj Singh]

TL;DR Summary

Do black-holes, or for that matter - does gravity / gravitational waves, get affected by expansion in any way?

Do black-holes, to a certain extent, have any unusual effects on expansion?

How will black-holes be affected especially in a scenario like the Big-Rip, being the last large-scale structures in the Universe, when expansion occurs to the extent of disintegration of matter?

I realize that my understanding of this matter and it's vast number of related concepts is rudimentary and incomplete.

Kindly forgive my ignorance and try to explain your thoughts in layman's terms.

Thank you for your time.

 

[phinds]

Summary: Do black-holes, or for that matter - does gravity / gravitational waves, get affected by expansion in any way?

As for the relationship between expansion and black holes, I'm reminded of a story Mark Twain told about being on a sea voyage in the far Southern seas when an elderly dowager spied an iceburg off in the distance and asked the captain what would happen if their ship collided with the iceburg. He replied "The iceburg, madam, would continue onwards as though nothing had happened"

 

[kimbyd]

Summary: Do black-holes, or for that matter - does gravity / gravitational waves, get affected by expansion in any way?

Do black-holes, to a certain extent, have any unusual effects on expansion?

How will black-holes be affected especially in a scenario like the Big-Rip, being the last large-scale structures in the Universe, when expansion occurs to the extent of disintegration of matter?

I realize that my understanding of this matter and it's vast number of related concepts is rudimentary and incomplete.

Kindly forgive my ignorance and try to explain your thoughts in layman's terms.

Thank you for your time.

Expansion is a large-scale phenomenon, which dominates the behavior of the universe on scales comparable to millions of light years and greater.

Black holes are tiny, compact objects. Currently very little of the mass in the universe is contained within black holes. A black hole the mass of, say, our Sun would have the exact same gravitational influence on its surroundings as our Sun does, with the only difference being that the black hole is way smaller (and dimmer).

There are black holes out there that are obscenely massive objects with masses billions of times the mass of our Sun, but they're still a small fraction of the masses of the galaxies they are contained within. So once you're away from the center of the galaxy (say, a few thousand light years), the gravitational influence of the black hole is completely irrelevant.

Black holes do other things besides interact with gravity, of course. When they are actively gobbling up matter that matter becomes obscenely bright, so bright that they can influence the entire galaxy they are contained within. But that's not an issue that interacts the expansion of the universe, just the shape of the galaxy (e.g. whether it becomes a spiral or elliptical galaxy). Either way, at their most violent, black holes only really influence matter within a few tens of thousands of light years.

Because the expansion is a description of how the universe behaves on scales of millions of light years and greater, black holes really don't influence the expansion in any meaningful way. To put it another way, whether there is a billion-solar-mass black hole in a galaxy or a billion solar-mass stars, the expansion will not be impacted. The galaxy will look different, but the expansion won't.

 

[eloheim]

There is a de Sitter–Schwarzschild metric wikipedia page that seems relevant to this question. For example, it describes scenarios where the black hole and cosmological horizons have merged:

The Nariai limit has no singularities, the cosmological and https://en.wikipedia.org/w/index.php?title=Black_hole_horizon&action=edit&redlink=1 have the same area, and they can be mapped to each other by a discrete reflection symmetry in any causal patch.

Sorry to say I can't add much to the discussion on this topic but there is literature out there about what happens to black holes in universes with runaway expansion.

 

[kimbyd]

There is a de Sitter–Schwarzschild metric wikipedia page that seems relevant to this question. For example, it describes scenarios where the black hole and cosmological horizons have merged:
Sorry to say I can't add much to the discussion on this topic but there is literature out there about what happens to black holes in universes with runaway expansion.

Yeah, but that's an unphysical situation that can't happen within our observable universe, as it requires a black hole with obscenely large mass. It's interesting as a thought experiment because weird stuff happens to the event horizon of the black hole in that limit, but it's not possible for a black hole of that size to be produced within our observable universe.

I think what you'd need for such a merger to happen would be to have as much mass within the cosmological horizon as you have energy density from the cosmological constant, and for all of that mass to be concentrated within a black hole. I just don't think such a thing can ever occur.

 

[phinds]

... it's not possible for a black hole of that size to be produced within our observable universe.

If it's not possible in our observable universe would it be possible somewhere in the rest of the universe or is that just impossible to say? It seems totally impossible to me but I know "impossible" is a word to be used with caution.

 

[kimbyd]

If it's not possible in our observable universe would it be possible somewhere in the rest of the universe or is that just impossible to say? It seems totally impossible to me but I know "impossible" is a word to be used with caution.

I honestly suspect it's impossible, but it's really hard to prove things like this are impossible. It's certainly a valid solution to the Einstein field equations. The question is how could you have a physical process which could produce such a result.

Consider, if you will, a very large black hole in an expanding universe with a cosmological constant. What are the requirements for the black hole to grow further so that its horizon can meet the cosmological horizon? Certainly in our universe it's just not feasible, because black hole growth gets quenched long before black holes can grow to such an absurd size: quenching happens because as the black hole absorbs matter, the matter it's absorbing becomes incredibly bright, which blows away nearby matter stopping further growth.

To get a horizon-scale black hole, at the very least you'd need to have a completely different configuration of matter than exists in our universe. I don't think we can state with confidence that such solutions are fundamentally impossible in any universe. This is more a suspicion I have because of the weirdness of the Nariai limit.

 

[PeterDonis]

I think what you'd need for such a merger to happen would be to have as much mass within the cosmological horizon as you have energy density from the cosmological constant, and for all of that mass to be concentrated within a black hole

More precisely, the condition for the key factor ##1 - \frac{2M}{r} - \frac{\Lambda}{3} r^2## to have multiple real roots, i.e., for the two horizons to be distinct, is that

$$
M < \frac{1}{3 \sqrt{\Lambda}}
$$

These are in geometric units, so ##\Lambda## here is an inverse length squared, i.e., it is the cosmological constant in conventional units multiplied by a factor ##G / c^2##. So the numerical value of ##\Lambda## based on our current best estimate of dark energy density, which is about ##7 \times 10^{-27} \ \text{kg / m}^3##, is about ##5 \times 10^{-54}##. This means ##M## has to be less than about ##1.5 \times 10^{26}##, and the units here are meters, so that's about ##10^{23}## solar masses. This is indeed comparable to the total mass within the cosmological horizon (indeed, I think it's larger--see below). And there is no possibility of all that mass being captured into a single black hole, since at the very least distinct galactic clusters are not gravitationally bound to each other.

 

[PeterDonis]

black hole growth gets quenched long before black holes can grow to such an absurd size: quenching happens because as the black hole absorbs matter, the matter it's absorbing becomes incredibly bright, which blows away nearby matter stopping further growth

I think there's actually a much simpler condition, which is, as I noted in my last post, that distinct galactic clusters, at least, are not gravitationally bound to each other: each one has sufficient kinetic energy relative to the other for escape.

The question is, how did that condition come about? And I think the answer is, heuristically speaking, given a universe that will not recollapse, the average kinetic energy of expansion must be at least as large as the average gravitational potential energy, which means that gravitationally bound systems should be smaller than the size of the observable universe. Or, to put it another way, for a black hole of comparable mass to the observable universe to form, there would have had to be a sufficiently large density perturbation in the early universe to trigger an entire region the size of the observable universe to gravitationally collapse into a single bound system, and such a fluctuation is extremely unlikely in a universe that will expand forever, and in fact did not happen early on in our universe--and now it's too late.

 

[kimbyd]

I think there's actually a much simpler condition, which is, as I noted in my last post, that distinct galactic clusters, at least, are not gravitationally bound to each other: each one has sufficient kinetic energy relative to the other for escape.

The question is, how did that condition come about? And I think the answer is, heuristically speaking, given a universe that will not recollapse, the average kinetic energy of expansion must be at least as large as the average gravitational potential energy, which means that gravitationally bound systems should be smaller than the size of the observable universe. Or, to put it another way, for a black hole of comparable mass to the observable universe to form, there would have had to be a sufficiently large density perturbation in the early universe to trigger an entire region the size of the observable universe to gravitationally collapse into a single bound system, and such a fluctuation is extremely unlikely in a universe that will expand forever, and in fact did not happen early on in our universe--and now it's too late.

The reason why those two numbers (total mass and the threshold mass) are comparable, by the way, is another consequence of the Cosmological Coincidence: the fact that dark energy and dark matter have similar densities right now.

In the past, when the universe was more dense, the total mass contained within the cosmological horizon set by ##\Lambda## was far larger than this limit, making it less obviously absurd that all matter within the observable universe might collapse into a single black hole of sufficient mass. If you look back to, say, ##z=100## when the matter density was a million times its current value but the cosmological constant was the same, you would have "only" needed to collect something like 0.01% of the matter density within the comological horizon into a single black hole to get this to work. This would require density perturbations vastly in excess of anything that existed in our observable universe, but they're not obviously absurd in any possible universe.

I think what you'd find if you looked at this in detail is that such large density perturbations in the early universe would have broken the assumptions of homogeneity and isotropy so completely that the big bang simply can't describe such a universe.