Black holes to explode due to evaporation?

[PeterDonis]

even then they'll need a long time (trillions of years, I think) to evaporate.

Much more than trillions. A one solar mass black hole has a Hawking evaporation time of about $10^{67}$ years.

 

[Vanadium 50]

Trillions ain't nothin;.. Heck, red dwarfs can last almost that long!

 

[phinds]

Also wasn't these evaporations supposed to exceed the lifetime of the universe?

No. They are expected to take a staggeringly long time but complared to the lifetime of the universe, which is presumably infinite in time, that amounts to pretty much nothing.

 

[sbrothy]

No. They are expected to take a staggeringly long time but complared to the lifetime of the universe, which is presumably infinite in time, that amounts to pretty much nothing.

Ah yes. Infinity divided by a very very long time still amounts to infinity I guess.

 

[phinds]

Ah yes. Infinity divided by a very very long time still amounts to infinity I guess.

You have this backwards. A huge amount of time compared to infinity is effectively zero.

 

[timmdeeg]

You have this backwards. A huge amount of time compared to infinity is effectively zero.

I think both is correct, two sides of the same coin.

 

[phinds]

I think both is correct, two sides of the same coin.

I think you're missing the point of what's being discussed. It's not the math of infinity, it's whether or not black hole evaporation requires the lifetime of the universe, or a comparatively short time.

 

[HansH]

"Gravitational wave hints black hole remnants as dark matter"
-- https://arxiv.org/abs/2303.07661

I think they mean that they don't really disappear at all no?

Also wasn't these evaporations supposed to exceed the lifetime of the universe?

from the summary:"the Universe might be filled with remnants of tiny primordial black holes, which formed with mass M<10^9g." suppose they exsist, then what happens if such final residue comes into contact with matter? does it then grow again?
if they exist they could easily be detected as it gives for example a gravitational force attracting (speaking in Newton terms) a mass of 1kg with 6.6 Newton at 0.1 meter distance.

 

[HansH]

I think you're missing the point of what's being discussed. It's not the math of infinity, it's whether or not black hole evaporation requires the lifetime of the universe, or a comparatively short time.

I think then you try to understand if such situation you can find in practice will be likely to occur or not. I assume the chance that something can occur is independent of the description what happens if it occurs. I think the discussion is about the last one.

 

[phinds]

I think then you try to understand if such situation you can find in practice will be likely to occur or not. I assume the chance that something can occur is independent of the description what happens if it occurs. I think the discussion is about the last one.

I have no idea what any of that means.

 

[HansH]

I have no idea what any of that means.

I mean the chance that some situation occurs has nothing to do with the behavior of that situation. for example I throw a stone from the roof that falls to the ground. then we can describe what happens according to the equations. But the chance that I have such a stone with all the molecules at the place is almost zero (I cannot find a second stone being the same as this stone) so now translating that to the situation: we have an evaporated black hole and discuss about how it is build and we have a parallel discussion about the chance that such an evaporated black hole can exist because it takes a very long time to create.

 

[HansH]

about the chance that such an evaporated black hole can exist because it takes a very long time to create.

suppose we have a particle accelerator with sufficient energy to create a nano black hole. (which is where some people are afraid of) then we can create the situation instantly, so I would propose to keep the discussion on topic discussiong the behavior of the evaporated black hole and not about how long it takes to get there, unless there is a good reason to.

 

[HansH]

No. Go read my previous posts again.It could be, provided the observer was capable of withstanding radiation of arbitrary intensity and had a rocket capable of providing an arbitrary amount of thrust indefinitely. Such an observer could, for example, "hover" at a constant altitude above the hole, and would see the rocket thrust required to maintain altitude continually decrease, until, after the final burst of light passed him, the thrust would be zero--he could turn off his rocket and just float in place in free fall.

is this in contradiction with #33? :
"Gravitational wave hints black hole remnants as dark matter"
-- https://arxiv.org/abs/2303.07661
the first gives no gravitational field left and the second does give gravitational field left I I understand it right.

 

[Ibix]

is this in contradiction with #33? :
"Gravitational wave hints black hole remnants as dark matter"
-- https://arxiv.org/abs/2303.07661
the first gives no gravitational field left and the second does give gravitational field left I I understand it right.

Again, that paper is assuming extensions to GR on which there is no consensus. Peter is (in the relativity forum) answering on the basis of GR.

 

[HansH]

ok, clear, so that also answers my question 'what happens if such final residue comes into contact with matter? does it then grow again? from #43 I suppose using GR nothing happens.
Then mij next question would be: suppose the mensioned extensions to GR were valid, what would happen then. then it would first evaporate radiating out a large amount of energy and then come to a stable situation with a restmass and a singularity alowing matter to fall in again and grow. And then it would radiate again with Hawking radiation and this cycle could repeat having a perpetuum mobile so that can't be true. (or should I ask this part of the question in a different forum part?)

edit: probably not a perpetuum mobile but a method to convert mass into pure enery.

 

[Nugatory]

next question would be: suppose the mensioned extensions to GR were valid, what would happen then.

We don’t know. None of these extensions are solid enough to support calculations with the level of detail and certainty that you are asking for, so we don’t know.
However….

then it would first evaporate radiating out a large amount of energy and then come to a stable situation with a restmass and a singularity alowing matter to fall in again and grow. And then it would radiate again with Hawking radiation and this cycle could repeat having a perpetuum mobile so that can't be true.

Makes no sense. The energy in the Hawking radiation is far away and moving farther away at the speed of light. It’s never coming back, so the only way for the hole to regrow is for us to bring in mass/energy from somewhere else - no perpetual motion or even free energy here.

 

[HansH]

However….Makes no sense. The energy in the Hawking radiation is far away and moving farther away at the speed of light. It’s never coming back, so the only way for the hole to regrow is for us to bring in mass/energy from somewhere else - no perpetual motion or even free energy here.

That is why I edited it: not a perpetuum mobile but a method to convert mass into pure enery :if you throw 1 gram of mass in first this mass falls to the center following the gravitational field, then the hawking radiation should start again (the energy coming out) because the mass is larger than the equilibrium and that process then stops when the equilibrium is reached. Such process looks strange as there seems to be a kind of hysterese in or delayed reaction. So I was wondering if that is already sufficient proof to skip this option.

 

[jbriggs444]

That is why I edited it: not a perpetuum mobile but a method to convert mass into pure enery :if you throw 1 gram of mass in first this mass falls to the center following the gravitational field, then the hawking radiation should start again (the energy coming out) because the mass is larger than the equilibrium and that process then stops when the equilibrium is reached. Such process looks strange as there seems to be a kind of hysterese in or delayed reaction. So I was wondering if that is already sufficient proof to skip this option.

So you have this 1 gram spherical blob of mass that you bring into the neighborhood of the singularity remaining from a black hole. Hopefully you have somehow managed to detect this uncharged, zero mass, singularity with no obvious gravitational effect before bringing the 1 gram mass into its neighborhood.

We assume that the black hole singularity will orbit in the interior of the 1 gram mass with a velocity smaller than the associated escape velocity -- rather slowly indeed.

The Schwarzschild radius of this black will be zero, of course. Its "gravitational attraction" will also be zero. The only way it is going to interact with the matter in the sphere is by some unspecified quantum interaction with a very short range -- it is going to eat one atom (or one sub-atomic particle) at a time.

Having acquired an atom, Hawking radiation will cause it to disgorge an equivalent amount of energy in something under about $10^{-91}$ seconds. That's for an atom with atomic weight 100. Eating something smaller gets you a shorter lifetime. The black hole singularity can then wander along to the next atom or atomic particle.

An interesting question arises: what velocity would a zero mass entity such as a black hole singularity acquire due to the recoil associated with Hawking radiation? Would this hypothetical black hole nucleus actually encounter a second atom? Or would it whizz away harmlessly?

It does not sound like a feasible device to me.

 

[HansH]

So you have this 1 gram spherical blob of mass that you bring into the neighborhood of the singularity remaining from a black hole. Hopefully you have somehow managed to detect this uncharged, zero mass, singularity with no obvious gravitational effect before bringing the 1 gram mass into its neighborhood.

It does not sound like a feasible device to me.

you talk about a different thing. we just discussed the difference between the "GR" approach and the "GR + extensions to GR" (see #49) we are discussing "GR + extensions to GR" here where it was assumed that there is a rsidual mass left ::"the Universe might be filled with remnants of tiny primordial black holes, which formed with mass M<10^9g." https://arxiv.org/abs/2303.07661

 

[HansH]

you talk about a different thing. we just discussed the difference between the "GR" approach and the "GR + extensions to GR" (see #49) we are discussing "GR + extensions to GR" here where it was assumed that there is a rsidual mass left ::"the Universe might be filled with remnants of tiny primordial black holes, which formed with mass M<10^9g." https://arxiv.org/abs/2303.07661

if you throw 1 gram of mass in first this mass falls to the center following the gravitational field, then the hawking radiation should start again (the energy coming out) because the mass is larger than the equilibrium and that process then stops when the equilibrium is reached. Such process looks strange as there seems to be a kind of hysterese in or delayed reaction. So I was wondering if that is already sufficient proof to skip this option.

I was further thinking about this process related to GR+extensions: https://arxiv.org/abs/2303.07661:
(please let me know if we should keep this discussion here or in a separate part of the forum related to theory development, and if so where?)

The extensions would then prevent to form a singularity as due to quantum effects the mass spreads out over a statistically defined volume (I would expect this statisticallty defined volume even can be seen at the event horizon in theory (but with extremely small chance of finding the mass there in case of a large black hole) and further outwards similar als an electron cloud around a nucleus of an atom.

This statistical distribution should than prevent the singularity. But as this volume is (effectively) still very small, there will be an event horizon. So from outside, the 1 gram of mass still feels the same gravitational field initially, but the field weakens (I mean increases less compared to GR only) as the mass falls further inwards due to the statistical distribution of the mass of the black hole. So further falling in towards the center, more and more mass will be located in shells outside the in falling mass untill in the center there is zero mass left as all the mass is outside similar as in the center of the earth. So no singularity and gravitational field is zero in the center (probably a bit noisy field because of the quantum fluctuations in the mass distribution).
so based on that I am not sure what are the consequences for Hawking radiation under this scenario. I would expect the hawking radiation is still there and the black hole evaporate faster and faster during evaporation as the basic machanism is not different, but as there is no singularity, all the mass will finally radiate away until the mass is so small that the event horizon disappears leaving a normal mass left only.
I also would expect that the infalling mass of a black hole is ripped apart and merges with the statistical mass distribution of the black hole mass. so the spagettification will go different as according to GR only and would be a statistically defined spagetty cloud of mass around the center of the black hole.

 

[PeterDonis]

I was further thinking about this process related to GR+extensions

Is this something in the paper you referenced? Or is it your own speculation?

please let me know if we should keep this discussion here or in a separate part of the forum related to theory development, and if so where?

If it's your own speculation, it's off limits anywhere at PF.

 

[HansH]

wel, we don't have such theory yet. so what do you think and why do you think I proposed it for Theory development. The reason is that I hoped someone with more overview of the latest progress in Physics would probably recognize some thoughts.

 

[PeterDonis]

we don't have such theory yet. so what do you think and why do you think I proposed it for Theory development

In other words, yes, it's your own speculation, which, as I said, is off limits here.

Thread closed.