I Black holes to explode due to evaporation?

[HansH]

TL;DR Summary

according to Hawking a black hole slowly evaporates and shrinks. as I understood there comes a moment when it explodes and the singularity disappears. is this true and if so, how is this triggered?

according to Hawking a black hole slowly evaporates and shrinks (when not feeded from outside with matter falling in). as I understood there comes a moment when it explodes and the singularity disappears. Is this true and if so, how is this triggered? and is there something such as a critical minimum mass?

 

[PeterDonis]

as I understood

From where? Do you have a reference?

there comes a moment when it explodes

More precisely, the rate of Hawking radiation increases as the hole gets smaller; in the final stage of evaporation the rate gets extremely rapid, to the point where it looks like an explosion.

and the singularity disappears.

The singularity is a global feature of the spacetime (more precisely, of the region of spacetime inside the hole). It doesn't "disappear". It just is not reachable from any events after the evaporation is complete.

 

[HansH]

not sure about a reference. If you say 'in the final stage of evaporation the rate gets extremely rapid' then when does it stop? Do I understand you right that the singularity always remains after evaporation? is there a residual mass then after evaporation? or are we talking about a singularity with mass=0?

 

[HansH]

I just came this this one: https://www.space.com/black-holes-general-relativity-gravity: As black holes evaporate, they get smaller and smaller and their event horizons get uncomfortably close to the central singularities. In the final moments of black holes' lives, the gravity becomes too strong, and the black holes become too small, for us to properly describe them with our current knowledge.

 

[PeterDonis]

If you say 'in the final stage of evaporation the rate gets extremely rapid' then when does it stop?

When the hole has finally evaporated.

Do I understand you right that the singularity always remains after evaporation?

A term like "always" does not make sense with respect to the singularity. The singularity is not a thing in space. It is a moment of time. That moment of time is to the future of all moments inside the black hole. But from outside the hole, that moment of time is not reachable after the black hole has evaporated (because the region of spacetime inside the hole is not reachable).

I just came this this one

Pop science sites are not good sources if you want to actually learn physics.

In the final moments of black holes' lives, the gravity becomes too strong, and the black holes become too small, for us to properly describe them with our current knowledge.

What they might be referring to here is that many physicists believe quantum gravity, when we actually have a good theory of it, will change our understanding of how black holes and black hole evaporation work. But until we have such a theory, all we have are the models that Hawking and others have constructed using our current theory of gravity, GR.

 

[HansH]

ok, but what does 'has finally evaporated.' mean. is the mass then 0?

 

[PeterDonis]

what does 'has finally evaporated.' mean. is the mass then 0?

To an observer who is to the future of the final burst of light that spreads outward from the final evaporation event, yes.

 

[HansH]

so To an observer who is to the future of the final burst of light then there is still a singularity but with mass=0? can this observer be someone standing beside this black hole final stage and observing its mass from outside?

 

[PeterDonis]

so To an observer who is to the future of the final burst of light then there is still a singularity but with mass=0?

No. Go read my previous posts again.

can this observer be someone standing beside this black hole final stage and observing its mass from outside?

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.

 

[Nugatory]

as I understood there comes a moment when it explodes...

Not quite. The rate at which energy is emitted is inversely proportional to the mass of the black hole, so as the black hole shrinks it evaporates away ever more quickly. Eventually the evaporation is fast enough that we describe the energy release as an "explosion".

...and the singularity disappears.

Well maybe, but we don't really know. The problem is that the math we use to calculate the rate of energy release makes some assumptions that probably do not hold as the mass of the hole goes all the way to zero. It's a safe bet that something interesting happens, but it may not be the interesting thing that we get from just carrying Hawking's equations all the way down to zero.

 

[HansH]

he could turn off his rocket and just float in place in free fall.

then I would assume the mass of the residue of the black hole =0 as there is floating in free space so then I do not understand what you mean with 'No. Go read my previous posts again.'

 

[Ibix]

Not all models of evaporating black holes include singularities. For those that do "past" and "future" is too simplistic a model of causality to describe where/when the singularity is. In the simplest model I'm aware of, if you don't enter the black hole then less and less of the singularity is reachable, until there comes a point where none of it is in your future lightcone. Some time after that you see the final Hawking radiation, but the singularity never enters your past lightcone, so is never unambiguously in your past. To the extent that there was ever "a place where the black hole was", there's nothing left there at that point.

 

[HansH]

The problem is that the math we use to calculate the rate of energy release makes some assumptions that probably do not hold as the mass of the hole goes all the way to zero. It's a safe bet that something interesting happens, but it may not be the interesting thing that we get from just carrying Hawking's equations all the way down to zero.

ok so that I interpret as that that is the edge of what we currently know.

 

[PeterDonis]

I would assume the mass of the residue of the black hole =0

There is no "residue of the black hole". The black hole is a region of spacetime. It is not a "thing" that "appears" or "disappears". It is a region of spacetime that is only accessible from certain other regions of spacetime. The black hole region of spacetime is not accessible from the region of spacetime to the future of the last light that gets emitted outward from the final evaporation.

I do not understand what you mean with 'No. Go read my previous posts again.'

I mean that I've already described the correct way to look at the singularity--and when you look at it that way, the questions you are asking don't even make sense. In particular, please read my post #5 (and most of all my second response in that post).

 

[PeterDonis]

The black hole is a region of spacetime.

The spacetime diagram in this Wikipedia article might help:

https://en.wikipedia.org/wiki/Black_hole_information_paradox#Black_hole_evaporation

The black hole is the region at the upper left, bounded by the singularity (jagged line) at the top (note that the singularity is horizontal, meaning it's spacelike--i.e., it's a moment of time, to the future of all events inside the black hole) and the event horizon (the 45 degree line going up and to the right, that meets the singularity at its right edge).

If you continue the 45 degree line of the event horizon further up past where it meets the singularity, that is the worldline of the last light emitted from the final evaporation of the black hole. The region of spacetime above (i.e., to the future of) that is flat--no black hole, no gravity, no "residue", no nothing: it's flat like the Minkowski spacetime of SR.

 

[DaveC426913]

A term like "always" does not make sense with respect to the singularity. The singularity is not a thing in space. It is a moment of time. That moment of time is to the future of all moments inside the black hole. But from outside the hole, that moment of time is not reachable after the black hole has evaporated (because the region of spacetime inside the hole is not reachable).

I think there is a discrepancy between answering "what is really happening" and "what is experienced by an observer."

Unless I am wrong, an external observer - who need know nothing about past or future light cones - sees a black hole shrink as it sheds Hawking radiation, even as its mass shrinks toward zero, flattening the local spacetime curvature, until at the last moment, it just poofs out, and all that is left is flat space and an expanding shell of radiation. Yes?

 

[HansH]

That moment of time is to the future of all moments inside the black hole. But from outside the hole, that moment of time is not reachable after the black hole has evaporated (because the region of spacetime inside the hole is not reachable).

So if I understand that well you say that you cannot have influence on that because it always remains a moment in future. but on the other hand nothing is left as seen from outside.

how does that relate to what is said in #10:
'The problem is that the math we use to calculate the rate of energy release makes some assumptions that probably do not hold as the mass of the hole goes all the way to zero.'

 

[Ibix]

how does that relate to what is said in #10:
'The problem is that the math we use to calculate the rate of energy release makes some assumptions that probably do not hold as the mass of the hole goes all the way to zero.'

All predictions made about black holes depend on GR, and even Hawking radiation is based on a semi-classical analysis. It all has to be wrong somewhere.

 

[timmdeeg]

Its an interesting discussion about something which doesn't exist, because the theory breaks down.

A common hope is that when quantum effects are taken into account in the vicinity of such extreme conditions of curvature where singularities are predicted by the classical theory, the singular nature of the spacetime geometry will be suppressed, leaving only well behaved spacetime structure.

 

[Ibix]

Its an interesting discussion about something which doesn't exist, because the theory breaks down.

Well - may not exist. We know GR has to be wrong somewhere, but we also know it's a very good predictor in many places. Exactly where it goes wrong and what actually would happen where it does is not known. At the fairly qualitative level of this discussion we might be right...

 

[Fra]

One can ask what an observer (say a particle lab), would hypothetical infer if from statistics if we could produce/prepare and make repeated experiments on small (subatomic) microscopic black holes? For example, how would they be distingiushed or classified in the overall phenomenology? It seems to me this can't be solved isolated from the other forces (as a quantum gravity only), as going up that energy level we need get pass and cross the domain where new physics may appear anyway.

From the perspective of high energy phenomenology, how would say a perphaps stable ot quasi-stable(as we don't know what QG will say, if there is a stable remnant or not), subatomic black hole "look like" from the outside? How is it different from a hypothetical elementary particle?

The assymmetry in the observing context (a human macro lab) and a subatomic blackhole, or a cosmological black hole are so huge, that I have not real faith in extrapolating the the mathematics of cosmological objects, to the subatomic domain. From the perspective of inference and empirics this is twisted in so many ways.

/Fredrik

 

[timmdeeg]

Well - may not exist.

Is there still a loophole that the singularity of a black hole could "exist"?
Wouldn't that mean that the theory breaks down at r = 0 but the singularity somehow "survives" though.

 

[PeterDonis]

if I understand that well you say that you cannot have influence on that because it always remains a moment in future.

No, that's not what I said. It's only a moment of time in your future if you are inside the hole. If you remain forever outside the hole, it's not. It's in a region of spacetime that becomes unreachable for you after a particular point on your worldline: the point at which your future light cone no longer includes any events inside the hole--or, in more ordinary language, the point after which you could no longer make yourself fall into the hole before it evaporated away even if you fell radially inward at the speed of light.

how does that relate to what is said in #10:
'The problem is that the math we use to calculate the rate of energy release makes some assumptions that probably do not hold as the mass of the hole goes all the way to zero.'

If we don't make those assumptions, we can't say anything about what happens because we don't have any other model of black hole evaporation to use. Everything I have said is using the model whose spacetime diagram I linked to, which is a model that is made using those assumptions.

Note, however, that there are other "black hole" models, such as the Bardeen "black hole" (a forum search on that term should turn up some previous threads on the topic), which aren't actually black holes at all (hence the scare quotes), because they don't have actual event horizons, only apparent horizons, and they don't have singularities. The objects in these models, however, look like black holes from the outside, and also evaporate in a way similar to the way Hawking envisioned.

It is quite possible that, as our understanding of physics in this area improves, we will find that some model like that is actually the correct description for the objects that we now refer to as "black holes". That would be nice because it would remove all the issues associated with the presence of an event horizon and singularity in the model whose spacetime diagram I linked to above.

 

[PeterDonis]

Its an interesting discussion about something which doesn't exist, because the theory breaks down.

A common hope is that when quantum effects are taken into account in the vicinity of such extreme conditions of curvature where singularities are predicted by the classical theory, the singular nature of the spacetime geometry will be suppressed, leaving only well behaved spacetime structure.

The "Bardeen black hole" type models I referred to in post #23 just now are an example of this kind of model. The missing piece is that we don't know at a microphysical level how the kind of stress-energy tensor that is required in the deep interior of such models gets produced.

 

[PeterDonis]

an external observer - who need know nothing about past or future light cones - sees a black hole shrink as it sheds Hawking radiation, even as its mass shrinks toward zero, flattening the local spacetime curvature, until at the last moment, it just poofs out, and all that is left is flat space and an expanding shell of radiation. Yes?

More or less. See the last part of my post #9.

 

[Ibix]

Is there still a loophole that the singularity of a black hole could "exist"?
Wouldn't that mean that the theory breaks down at r = 0 but the singularity somehow "survives" though.

No, I agree the singularity is implausible. I was only thinking of "black holes radiate away leaving nothing behind", which is true for Hawking radiation and might turn out to be true for a full quantum gravity model.

 

[Vanadium 50]

We know GR has to be wrong somewhere,

I don't think we know that. QM could be wrong somewhere.

, to the point where it looks like an explosion.

It does, but not like explosions we are familiar with, especially on astronomicall scales.

It's brighter than the sun = but only for 40 nanoseconds. The energy in that 40 ns is large by terrestrial scales - kilotons - but small on astronical scales. If we had an evaporation in our galaxy, I doubt it would be visible to the naked eye.

 

[Nugatory]

I don't think we know that. QM could be wrong somewhere.

QM could be - probably is - wrong somewhere but that doesn't get to us to "GR is not wrong somewhere". The two theories work very well in their own domains but those domains have so little overlap that there's no reason to trust either at the intersection of strong spacetime curvature and small distances,

 

[HansH]

at #26: can you explain what 'implausible' means? if I google on 'implausible', the only link I get from google is this topic:

Reference: https://www.physicsforums.com/threa...lode-due-to-evaporation.1051054/#post-6868746

 

[Ibix]

at #26: can you explain what 'implausible' means? if I google on 'implausible', the only link I get from google is this topic:

https://dictionary.cambridge.org/dictionary/english/implausible

 

[Ibix]

I don't think we know that. QM could be wrong somewhere.

I agree with Nugatory that QM and GR being inaccurate are not mutually exclusive options.

To be formal, then, we know GR contains singularities, and inevitably so in spacetimes that don't violate energy conditions. So we either accept that the real world contains singularities or GR is missing something, and I think it's a fairly small minority that would plump for the former. However, even taking the latter position doesn't preclude GR+Hawking radiation being a reasonably accurate description of black hole evaporation, because we don't know the limits of its domain of applicability.

 

[timmdeeg]

at #26: can you explain what 'implausible' means?

https://www.linguee.de/deutsch-englisch/search?source=auto&query=implausible is helpful.

 

[sbrothy]

[...] According to Hawking a black hole slowly evaporates and shrinks. as I understood there comes a moment when it explodes and the singularity disappears. is this true and if so, how is this triggered? [...]

"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?

 

[Ibix]

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

Yes or no, depending on your preference for which candidate quantum theory of gravity is correct, I think. The paper proposes ways of detecting the remnants if they do exist.

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

For stellar mass black holes, yes. They actually absorb more CMB radiation than they emit Hawking radiation, so will actually continue to grow until the CMB temperature falls below their blackbody temperature. And even then they'll need a long time (trillions of years, I think) to evaporate. But the blackbody temperature, and the strength of the Hawking radiation, is higher for small black holes. So small holes have less mass to lose and they lose it faster. If micro black holes did form in the early universe they could have evaporated away to nothing (or whatever they actually do...) by now.

 

[Fra]

Another interesting angle here, when asking about the fate of the BH remnants, are these ideas, just a random paper, there are more of them, mostly i string theory though. But as I see it, the concept is not necessarily dependent on string theory.

Cosmic Natural Selection, Leonard Susskind
"I make a number of comments about Smolin's theory of Cosmic Natural Selection.
...
That raises the question of what exactly is a black hole? One of the deepest lessons that we have learned over the past decade is that there is no fundamental difference between elementary particles and black holes. As repeatedly emphasized by ’t Hooft [10][11][12], black holes are the natural extension of the elementary particle spectrum. This is especially clear in string theory where black holes are simply highly excited string states. Does that mean that we should count every particle as a black hole?..."
-- https://arxiv.org/abs/hep-th/0407266

and

A Correspondence Principle for Black Holes and Strings​

https://arxiv.org/abs/hep-th/9612146

/Fredrik

 

[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.