Can there be slowly-falling accretion disks in black holes?

[Suekdccia]

TL;DR Summary

Can there be slowly-falling accretion disks in black holes?

Black holes accrete mass around them and it falls gradually up to the even horizon where mass is trapped by the black hole forever. However, the rate of mass falling from the accretion disk to the black hole ranges from being very fast to very long-lived, depending on various conditions

Meanwhile, black holes are continously being evaporated by the emission of Hawking radiation, but the rate is very slow, and it is even slower for bigger and more massive black holes

Can there possibly be black holes that have a disk of accretion of mass where the rate of infalling mass is very slow and approximately matches the rate of Hawking radiation emission?

 

[Ibix]

Currently no, because the CMB infall is higher than the Hawking emission for even a stellar mass black hole. Even an isolated hole is growing, not evaporating.

In principle you could have a small enough hole that the Hawking radiation matched the CMB infall, but we don't know of any process to produce holes in that mass range. And the CMB temperature continues to drop, so the balance would only be transient.

 

[Vanadium 50]

In principle you could have a small enough hole that the Hawking radiation matched the CMB infall, but we don't know of any process to produce holes in that mass range.

And I don't think they would last. These BH's are moon-sized, and have evaporation times in the seconds. Yes, the evaporation may be perfectly balanced by the CMB infall, but next year they will be out of balance by a part in a few billion. Which decreases the evaporation time to decades.

The next year, the imbalance is a factor of 2 worse. And as time goes on, the CMB cools and the BH heats up. And you have a runaway. My guess is they only last a few decades before "popping".

And of course, any BH just a little smaller "popped" in the past.

 

[Suekdccia]

And I don't think they would last. These BH's are moon-sized, and have evaporation times in the seconds. Yes, the evaporation may be perfectly balanced by the CMB infall, but next year they will be out of balance by a part in a few billion. Which decreases the evaporation time to decades.

The next year, the imbalance is a factor of 2 worse. And as time goes on, the CMB cools and the BH heats up. And you have a runaway. My guess is they only last a few decades before "popping".

And of course, any BH just a little smaller "popped" in the past.

The imbalance would be due to the redshift of CMB?

But wouldn't this be possible with regular matter accreting to the black hole with a rate that would compensate for such balance? (as far as I know accretion rates can change and are not constant, so could it possibly change with time so that it balances with the CMB avoiding the evaporation of the black hole?)

 

[phinds]

Can there possibly be black holes that have a disk of accretion of mass where the rate of infalling mass is very slow and approximately matches the rate of Hawking radiation emission?

I don't think you understand the rate of Hawking emissions. As you can see, the previous two answers haven't even addressed the question of accretion discs because the in-fall from the CMB ALONE is more than enough to totally swamp Hawking Radiation for all but really tiny black holes.

An accretion disk would be many many many orders of magnitude stronger than Hawking Radiation. You should research how long it takes for the typical BH to evaporate WITHOUT an accretion disk.

 

[Suekdccia]

I don't think you understand the rate of Hawking emissions. As you can see, the previous two answers haven't even addressed the question of accretion discs because the in-fall from the CMB ALONE is more than enough to totally swamp Hawking Radiation for all but really tiny black holes.

An accretion disk would be many many many orders of magnitude stronger than Hawking Radiation. You should research how long it takes for the typical BH to evaporate WITHOUT an accretion disk.

I understand that the rate of Hawking radiation emission is very slow. That's why I asked about an accretion disk having a very slow infall rate.

As you can see, the CMB radiation infall would outpace the Hawking radiation rate. But the CMB would be redshifted as time passes by, so even if the CMB infall rate would be the same as the Hawking radiation rate, it would stoo being at equilibrium, as eventually there would be more energy exiting the black hole than entering it. So, if there was an accretion disk with an infall rate that woukd be very slow but that would compensate to the CMB refshift, then it should be at equilibrium.

Besides, in the future, CMB radiation would be so redshifted that it would virtually add no energy. So, perhaps another way to think about my question is in a scenario where the universe has no CMB or that it has been redshifted all the way down

 

[phinds]

So, perhaps another way to think about my question is in a scenario where the universe has no CMB or that it has been redshifted all the way down

Irrelevant in all practical terms. The absence of the CMB would likely reduce the time of a BH's evaporation by a few orders of magnitude, so for supermassive BHs, say it would drop from a range of 1E60 -> 1E80 years all the way down to a range of 1E50 -> 1E70 years.

I can't imagine it would be possible for an accretion disc to even BEGIN to last that long.

 

[Suekdccia]

Irrelevant in all practical terms. The absence of the CMB would likely reduce the time of a BH's evaporation by a few orders of magnitude, so for supermassive BHs, say it would drop from a range of 1E60 -> 1E80 years all the way down to a range of 1E50 -> 1E70 years.

I can't imagine it would be possible for an accretion disc to even BEGIN to last that long.

Would it be impossible to have a stable accretion disk (with a very slow infall rate) for such a long time?

Perhaps if there was a slow but continuous source of matter falling to the accretion disk?

Or what about smaller black holes with smaller evaporation rates? Perhaps then the accretion disk would be stable?

 

[Ibix]

It depends what you mean by "possible".

Can you define initial conditions such that the infall of matter is steady and exactly matches the evaporation rate long term? Almost certainly - I don't know if you can patch evaporation into an ingoing Vaidya metric, but that's the sort of thing I have in mind.

Can such a thing occur without being carefully set up? I wouldn't go as far as saying no because weird things do happen. But I would use the strongest term short of "no" that I could think of. And it can't hapen at all until you have a black hole that's hotter than the CMB.

 

[phinds]

Would it be impossible to have a stable accretion disk (with a very slow infall rate) for such a long time?

You keep asking the same question over and over. Do you have some intellectual investment in the answer being yes? My answer is ... of course not, with the very short-term exception stated in the last part of this response.

Perhaps if there was a slow but continuous source of matter falling to the accretion disk?

WHY? HOW ? How do you make infall become slow ???

Or what about smaller black holes with smaller evaporation rates? Perhaps then the accretion disk would be stable?

Hawking Radiation gets BIGGER for smaller black holes.

The only way to get a "stable" accretion disk would be to have matter falling into the accretion disk at the same rate as the rate of matter falling from the accretion disk into the BH. This is not sustainable over even a fraction of the life of a BH. You seem to continue not to take into account the staggeringly long life of BHs.

 

[Vanadium 50]

I can't imagine it would be possible for an accretion disc to even BEGIN to last that long.

Why not? That's almost as long as this thread has been going in circles.

If you have an accrerion disk that weighed one solar mass, 10^60 years means one lone atom falls in every 10,000 years.

 

[phinds]

If you have an accrerion disk that weighed one solar mass, 10^60 years means one lone atom falls in every 10,000 years.

Well, shoot ... that means that to get one entire atom to fall in every single year, we just need an accretion disk of 10,000 solar masses.