"Black holes can only get bigger" - huh?

[Terrr]

TL;DR Summary

"Black holes can only get bigger" - what about Hawking radiation?

Lately I see these kinds of articles:

https://mysteriousuniverse.org/2021...AzA1y5_SznqRtVf6ePQlJqPFaGRMIK3TvV4SqqzXt96Bg

As far as I understood, it has been pretty much accepted that tiny black holes not only reduce their surface area over time due to the Hawking radiation, but can evaporate completely. How is that consistent with the "Black holes can only get bigger" thing?

 

[phyzguy]

Tiny black holes do not appear to exist in our universe. The smallest black holes that we know about are several solar masses in size. All real black holes only grow with time. Any reduction of their size due to Hawking radiation is unmeasurably small.

 

[phinds]

Any reduction of their size due to Hawking radiation is unmeasurably small.

Yes, but it will at an unimaginably long time from now (something like 10E80 years) make the hole evaporate, according to the currently accepted theory.

 

[Terrr]

"Evaporation effects are very small" still contradicts the "Black holes can only get bigger" thing.

 

[phinds]

"Evaporation effects are very small" still contradicts the "Black holes can only get bigger" thing.

Correct. phyzguy is correct that at this time in the current universe, they only get bigger but as I said above, they WILL evaporate over time (LOTS of time)

 

[Terrr]

phinds, I am sorry, but the "Black holes can only get bigger" is presented in the article not as "effect in present" but as the consequence of the 2nd law of thermodynamics - that is, as a fundamental law of physics.

I presume that's incorrect.

 

[phinds]

phinds, I am sorry, but the "Black holes can only get bigger" is presented in the article not as "effect in present" but as the consequence of the 2nd law of thermodynamics - that is, as a fundamental law of physics.

I presume that's incorrect.

Yes, it is incorrect. ALL objects radiate **, including black holes. The issue of whether or not something changes size over time is based on the balance of the radiation it emits vs the radiation it receives, plus any other mechanism that adds or subtracts matter. Right now, Hawking Radiation contributes such an utterly trivial amount to that equation that it is negligible but when all the stars have died the equation starts to favor Hawking Radiation.

**EDIT: except objects at absolute zero, if there is such a thing

 

[Nugatory]

Lately I see these kinds of articles:

Just because you see them doesn't mean that you have to waste your time reading them.

And seriously, kidding aside, these popularizations are well-intentioned but often oversimplify to the point of being misleading, and this one is no exception. What's really going here is that the black hole merger data shows that when two black holes merge the results is a single black hole larger than the sum of the two parts. That's an interesting and important result; every physicist looking at the actual published results it will understand that it is unrelated to whether Hawking radiation might eventually shrink a black hole sometime in the distant future. Unfortunately this nuance was lost when msteriousuniverse.com provided a layman-friendly summary.

You will get much better explanations (although getting and understanding them will be more work) here and from real textbooks.

 

[PeterDonis]

the "Black holes can only get bigger" is presented in the article not as "effect in present" but as the consequence of the 2nd law of thermodynamics - that is, as a fundamental law of physics.

First, the second law is not a "fundamental" law of physics; it's a consequence of the fundamental laws under particular conditions (roughly, that the initial conditions of the system are carefully chosen to be low entropy).

Second, the version of the second law that says that black holes can only get bigger is a classical version, not a quantum version. In the presence of quantum effects, the second law no longer says that; all it says is that the overall entropy of black hole + radiation increases. This is perfectly consistent with a black hole getting smaller as it emits Hawking radiation: the entropy increase in the radiation more than counterbalances the entropy decrease in the black hole as it gets smaller.

 

[Keith_McClary]

the black hole merger data shows that when two black holes merge the results is a single black hole larger than the sum of the two parts.

Are there theoretical reasons that they can't splatter into three holes?

 

[phinds]

Are there theoretical reasons that they can't splatter into three holes?

Nothing can get out of a black hole, not even another black hole.

 

[Keith_McClary]

Nothing can get out of a black hole, not even another black hole.

It has been suggested that there may even be a regime where a third or more black holes are formed during the interaction of the two black holes before they scatter, essentially due to the strong focusing of gravitational waves by the shock-fronts representing the boosted black holes [94]. This would be an astonishing addition to the phenomenology of the two body problem in general relativity if the scenario can be realized.

 

[PeterDonis]

Are there theoretical reasons that they can't splatter into three holes?

Yes. See below.

Nothing can get out of a black hole, not even another black hole.

You can't have a black hole inside another black hole.

A black hole is a region of spacetime that can't send light signals to infinity. Once you're inside such a region, there can't be another such region inside it; that makes no sense.

Similarly, such a region can't possibly split into two such regions, since that would mean some events at the "split" would be able to send light signals to infinity.

 

[PeterDonis]

It has been suggested that there may even be a regime where a third or more black holes are formed during the interaction of the two black holes before they scatter, essentially due to the strong focusing of gravitational waves by the shock-fronts representing the boosted black holes [94]. This would be an astonishing addition to the phenomenology of the two body problem in general relativity if the scenario can be realized.

None of this involves a black hole splitting into two or more. If a third black hole forms while two holes are scattering off each other, the third hole is outside both of the other two.

 

[phinds]

You can't have a black hole inside another black hole.

I know, I was just making a quickie response to the idea of two BH's merging and a 3rd being emitted out of the merger

 

[PeterDonis]

I was just making a quickie response

A quickie response that has an obvious implication that's false, IMO, is not very useful. That's why I responded with a correction.

 

[Fra]

As far as I understood, it has been pretty much accepted that tiny black holes not only reduce their surface area over time due to the Hawking radiation, but can evaporate completely. How is that consistent with the "Black holes can only get bigger" thing?

Set aside the issue of popular writings. I think that just as it is questionable to extrapolate QM rules to cosmology, similar care should also be taken when extrapolating what we think we know about large black holes, to the speculative notion of microscopic or Planck scale black holes.

As long as we do not have a unification of QM and GR I think its hard to make too certain inferences about thes new domain where both things are at play. Maybe or maybe not some quantization rules will at some point stop a small black hole from fully evaporating and remain some remnant with unknown interaction properties, and would it still really be classified as a black hole, relative to a Earth based observer?

/Fredrik

 

[PeterDonis]

As long as we do not have a unification of QM and GR I think its hard to make too certain inferences about thes new domain where both things are at play.

This is an issue of whether our current models are correct. But the OP's question was about what our current models say. Our current models say what I said in post #9.

 

[stevendaryl]

You can't have a black hole inside another black hole.

That's true, but ...

Imagine that you have an absolutely enormous black hole. Say, one with a Schwarzschild radius of $10^{10^{10}}$ light-years. Then inside such a black hole, the tidal forces would be very mild for a considerable length of time. Eventually, anyone inside will be crushed by the singularity at $r=0$, but in the region with $r$ much greater than zero (but still inside the Schwarzschild radius), conditions will look a lot like flat spacetime, at least in a small region (say, less than a million light years). So in such a region, there might be a ball of dust (by assumption, it only interacts gravitationally) massive enough to collapse into a black hole (with a modest Schwarzschild radius of, say, 100 kilometers) if it were actually in flat spacetime. So what happens to this ball of dust?

 

[PeterDonis]

conditions will look a lot like flat spacetime

Locally, yes, but that local region will be falling towards the singularity at $r = 0$. So its extent in time is limited.

what happens to this ball of dust?

By the time it has collapsed to zero radius within itself, it will also have hit the global singularity at $r = 0$. In the interim, it is possible for it to form an apparent horizon, but that apparent horizon will not be a global event horizon, nor will it have any relationship to one.

Note that the collapse you describe cannot happen in a flat region of spacetime. If the collapse you describe is happening in a region of spacetime, that region of spacetime is not flat, not even locally (except that you can find "local" patches much, much smaller than the collapsing region that can be locally viewed as flat--but their extent in time will be tiny).

 

[PeterDonis]

In the interim, it is possible for it to form an apparent horizon, but that apparent horizon will not be a global event horizon, nor will it have any relationship to one.

Note also that, for it to be possible at all for such an apparent horizon to form way inside a global event horizon, which also has an apparent horizon associated with it, spacetime inside the global event horizon cannot be vacuum; in fact, IIRC, the SET inside the global event horizon has to violate energy conditions (i.e., it has to be some form of "exotic matter") in order for it to be possible to have multiple apparent horizons.

 

[stevendaryl]

Locally, yes, but that local region will be falling towards the singularity at $r = 0$. So its extent in time is limited.By the time it has collapsed to zero radius within itself, it will also have hit the global singularity at $r = 0$. In the interim, it is possible for it to form an apparent horizon, but that apparent horizon will not be a global event horizon, nor will it have any relationship to one.

Note that the collapse you describe cannot happen in a flat region of spacetime. If the collapse you describe is happening in a region of spacetime, that region of spacetime is not flat, not even locally (except that you can find "local" patches much, much smaller than the collapsing region that can be locally viewed as flat--but their extent in time will be tiny).

I don't mean flat everywhere, I mean nearly flat well away from the ball of dust. So there would be some region centered on the center of the ball of dust that would be approximately described by the Schwarzschild radius.

 

[256bits]

I don't mean flat everywhere, I mean nearly flat well away from the ball of dust. So there would be some region centered on the center of the ball of dust that would be approximately described by the Schwarzschild radius.

Interesting concept.
The tidal forces at the horizon would not be very strong.
So two neutron stars on a rotating path to a collision( and perhaps forming a black hole ) approach the enormous one , and if the collision happens just within the horizon, they 'should' form a black hole within the gigantic black hole before reaching the singularity, one would think.
But what happens if a stellar black hole approaches and crosses the horizon. From outside, the gigantic black hole increases its size. Doesn't seem right that the stellar back hole would travel as a black hole to the gigantic singularity. Does it loose its own horizon to the enormous one?

 

[PeterDonis]

there would be some region centered on the center of the ball of dust that would be approximately described by the Schwarzschild radius.

I think you mean the Schwarzschild geometry. However, the physical interpretation of the horizon in the Schwarzschild geometry as an event horizon (as opposed to just an apparent horizon) is only valid if the geometry is not just a small patch surrounded by some other spacetime; the "infinity" in the Schwarzschild geometry has to be the actual infinity of the global spacetime for the "event horizon" interpretation to be valid.

 

[PeterDonis]

two neutron stars on a rotating path to a collision( and perhaps forming a black hole ) approach the enormous one , and if the collision happens just within the horizon, they 'should' form a black hole within the gigantic black hole before reaching the singularity, one would think.

They can form a region surrounded by an apparent horizon (but, as I said in an earlier post, I think you can only have one apparent horizon inside another if energy conditions are violated, i.e., if there is exotic matter present, which ordinary neutron stars would not have), but they cannot form a region surrounded by an event horizon, since, for the reasons I have already given, it is impossible (as in "doesn't even make sense") to have one event horizon inside another.

Does it loose its own horizon to the enormous one?

Yes; the stellar mass black hole's horizon just merges with the gigantic black hole's horizon. In a spacetime diagram, where the horizon of a single black hole is like a cylinder extending vertically, a merger of two black holes has a single horizon that looks like a pair of trousers; the legs are below (where there are two separate black holes) and they merge into a single cylinder above (where there is just one black hole).

 

[256bits]

They can form a region surrounded by an apparent horizon (but, as I said in an earlier post, I think you can only have one apparent horizon inside another if energy conditions are violated, i.e., if there is exotic matter present, which ordinary neutron stars would not have), but they cannot form a region surrounded by an event horizon, since, for the reasons I have already given, it is impossible (as in "doesn't even make sense") to have one event horizon inside another.Yes; the stellar mass black hole's horizon just merges with the gigantic black hole's horizon. In a spacetime diagram, where the horizon of a single black hole is like a cylinder extending vertically, a merger of two black holes has a single horizon that looks like a pair of trousers; the legs are below (where there are two separate black holes) and they merge into a single cylinder above (where there is just one black hole).

Thanks. That's pretty much what I thought.
You explain it quite well.

 

[Buzz Bloom]

when all the stars have died the equation starts to favor Hawking Radiation.

It would be interesting to compare the time in the future when all the stars have died with the time at which the Hawing radiation temperature is greater than the CMB temperature. I think that at the time all the stars have died the the Harking radiation temperature of a BH at its maximum size will still be less than the CMB temperature. This means that the BH will continue to grow as a result of absorbing CMB photons until a much later time when he CMB temperature finally gets to be less than the Hawking radiation temperature.

 

[Vanadium 50]

For most of the universe, there is more energy in the CMBR than starlight. (Not on Earth, of course, because we are a billion times closer to a star than average).

The cross-over size for a BH to grow or shrink today is about the mass of the moon. Heavier, they grow. Lighter, they shrink.

 

[phinds]

It would be interesting to compare the time in the future when all the stars have died with the time at which the Hawing radiation temperature is greater than the CMB temperature. I think that at the time all the stars have died the the Harking radiation temperature of a BH at its maximum size will still be less than the CMB temperature. This means that the BH will continue to grow as a result of absorbing CMB photons until a much later time when he CMB temperature finally gets to be less than the Hawking radiation temperature.

I'm not so sure about that. The thing is, by the time the stars have all died, accelerated expansion will mean that BH's are in an Observable Universe that only has at most a single galactic cluster of dead stars. The CMB as we think of it today will have receded to nothing but the emissions from that cluster so will go to essentially zero within a few tens of millions of years, which is nothing compared to the time it took to get there.

 

[Buzz Bloom]

by the time the stars have all died, accelerated expansion will mean that BH's are in an Observable Universe that only has at most a single galactic cluster of dead stars

I am interpreting the quote as saying that a good approximation about the ultimate mass of a surviving BH is the total mass of a galactic cluster, or perhaps just all the baryonic mass plus just perhaps some very small amount of the dark matter. Do you have any rough approximate thoughts about (1) the age A of the universe when the Milky Way's galactic cluster will reach this single BH state which of course involves the slow collapse of orbits due to gravitational wave generation, and (2) the mass M of this BH?

 

[phinds]

I am interpreting the quote as saying that a good approximation about the ultimate mass of a surviving BH is the total mass of a galactic cluster, or perhaps just all the baryonic mass plus just perhaps some very small amount of the dark matter.

That's not what I'm saying. The BH at the center of the Milky Way is approximately 2% or so of the total mass of the Milky Way and I see no reason why that would be substantially different down the road.

Do you have any rough approximate thoughts about (1) the age A of the universe when the Milky Way's galactic cluster will reach this single BH state which of course involves the slow collapse of orbits due to gravitational wave generation, and (2) the mass M of this BH?

No, but I didn't consider the possibility that the BH would consume the galaxy. Are you sure that happens?

The ages give for the evaporation of BH's ranges from 10E60 to 10E80 years, presumably depending on their size now.

 

[Buzz Bloom]

No, but I didn't consider the possibility that the BH would consume the galaxy. Are you sure that happens?

I am pretty sure that it happens in principal, but I am somewhat uncertain about the rate of orbit decay. A small mass in orbit about the large mass will have it's average orbit radius reduce at a very slow rate, but it will it eventually be absorbed by the large mass. I am not sure how the time for the complete combining of masses into a single super-big BH would take. At one time I had found a GR equation from which this might be calculated with some resemblance of approximation, but I can't find that equation now. What can be calculated is the Temperature of such a black hole based on the calculation of it's total mass.

Here is the mass of the MW according to Wikipedia:

M = 10¹² M_sun.​

Andromeda is about the same size, and there are about 80 small galaxies in the group. If we ignore these small galaxies and also ignore dark matter, a conservative estimate of the group mass is

M ~= 4 10¹¹ M_sun.​

The radiation temperature from such a BH is

T = 6*10^-8/(4 10¹¹) = 1.5 10^-19 Kelvin​

See https://jila.colorado.edu/~ajsh/bh/hawk.html​

and https://en.wikipedia.org/wiki/Hawking_radiation .​

From this the T value, an approximate scale factor a corresponding to T can be calculated.

a = 3/(1.5 10^-19) = 2 10²⁰.​

Using an admittedly simplified form of the Friedmann equation

da/dt = H₀​

t = a / H₀ = (2 10²⁰) (14 10⁹ yr) = 3 10³⁰ yr[/SUP]​

See https://en.wikipedia.org/wiki/Friedmann_equations#Detailed_derivation​

where​

Ω_k = Ω_m = Ω_r = 0, Ω_Λ = 1 .​

That is as far as I can go now. To complete the analysis I also need to calculate the length of time it takes a BH to change its size due to Hawking radiation changing between two specific temperatures. I also need to calculate/estimate the time for the formation of the single BH from the MW group.

 

[Sunil]

Hawking radiation is up to now only a theoretical prediction, with a quite dubious "derivation". This "derivation" has a very serious problem named "trans-Planckian". That means, one has to assume that the more or less established semi-classical approximation holds for much much smaller distances than Planck length. This can be easily proven by considering modifications of GR which make a difference only in the trans-Planckian domain but have no Hawking radiation.

See Paranjape, A., Padmanabhan, T. (2009). Radiation from collapsing shells, semiclassical backreaction and black hole formation, Phys.Rev.D 80:044011, arxiv:0906.1768v2 for the mathematics.

 

[Buzz Bloom]

Hawking radiation is up to now only a theoretical prediction, with a quite dubious "derivation".

I am wondering about the division of opinions on this topic. Can you make a rough estimate of the fraction of physicists who have each of one of three logically possible opinions?
1. Hawking radiation is definitely more likely than not to be a real possible phenomenon.
2. Hawking radiation is definitely more likely than not to not be a real possible phenomenon.
3. It is more-or-less equally likely that Hawking radiation is or is not a real possible phenomenon.

 

[PeterDonis]

I am wondering about the division of opinions on this topic.

The most important thing to know is that they are all just opinions at this point; we have no way of experimentally testing for Hawking radiation now or in the foreseeable future. The final determination will be the experimental test, not any physicist's opinion.

That said, while I don't have an estimate of the fractions of each, I believe there have been multiple papers published advocating each of your three options.