Naked Science Forum

Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: 5ASE on 17/04/2019 14:36:54

Title: How do black holes evaporate?
Post by: 5ASE on 17/04/2019 14:36:54
As far as I understand the popular science explanation of black hole evaporation, quantum fluctuations of vacuum at the event horizon create a pair of matter-antimatter particles. One escapes thus reducing the mass of the black hole. So far so good. However, just outside the horizon, the same effect must be continually feeding new particles into the black hole. The outside sphere is somewhat bigger, there must be more mass entering than leaving.

I suspect he popular explanation must be leaving out some important details?
Title: Re: How do black holes evaporate?
Post by: Janus on 17/04/2019 16:36:06
As far as I understand the popular science explanation of black hole evaporation, quantum fluctuations of vacuum at the event horizon create a pair of matter-antimatter particles. One escapes thus reducing the mass of the black hole. So far so good. However, just outside the horizon, the same effect must be continually feeding new particles into the black hole. The outside sphere is somewhat bigger, there must be more mass entering than leaving.

I suspect he popular explanation must be leaving out some important details?
One thing to keep in mind is that the formation of virtual particles just outside the event horizon comes from "borrowed" energy. Under normal circumstances, these particles only exist briefly, before rejoining and returning this borrowed energy. It is a quirk of QM that allow this to happen without violating energy conservation. 
If, however, one of the particles crosses inside the event horizon before the rejoining can occur ( it does not matter whether it is the particle or anti-particle),  You are left with a lone particle.  The energy books must be balanced in order for this particle to continue to exist, and this come from the mass of the BH.  One of the virtual particle pair has become a real particle at the expense of the BH.  This particle may escape, or more likely interact with another particle which produces light radiation that does escape the region near the event horizon. You end up with some "leakage" of radiation.
That being said, only black holes below a certain size would end up experiencing net shrinkage through Hawking radiation.  One of the features of Hawking radiation is that it increases as the mass of the Black hole decreases. Large black holes lose mass through Hawking radiation at a much lesser rate than they gain it from other sources.  Any stellar sized black hole, even if far away from any matter that it could absorb would still be gaining mass from just the cosmic background radiation faster than it lost it through Hawking radiation.   
For a black hole to lose mass faster than it gains it from the CMBR, it could not be any more massive than our Moon.
This is much smaller than any black holes that form today, but there is some speculation that small or "quantum" black holes could have formed during the early universe.  It is possible that some of them survived to our time.

Even present day large black holes are subject to eventual evaporation.  As the universe continues to expand, it cools which decreases the intensity of the background radiation.  At some point it will cool enough for stellar mass black holes to begin to evaporate as they lose mass faster than they gain it even through the CMBR.   But we are talking about really, really, really long time scales.
Title: Re: How do black holes evaporate?
Post by: Halc on 17/04/2019 16:55:52
If, however, one of the particles crosses inside the event horizon before the rejoining can occur ( it does not matter whether it is the particle or anti-particle),  You are left with a lone particle.
A question on this one.  A black hole is created with X mass of almost pure matter, and yet the Hawking radiation seems to return it as an even mix of matter/anti-matter.  This seems to violate some sort of balance between the two (which is already inexplicably imbalanced by the predominance of matter over antimatter).  Is there any sort of balance law that says that matter cannot be changed into antimatter without some sort of equal/opposite reaction?  If what you say is true, Hawking radiation seems to violate that balance law as it creates an even mix out of what was once mostly matter.  It feels wrong.
Title: Re: How do black holes evaporate?
Post by: Janus on 17/04/2019 17:34:52
If, however, one of the particles crosses inside the event horizon before the rejoining can occur ( it does not matter whether it is the particle or anti-particle),  You are left with a lone particle.
A question on this one.  A black hole is created with X mass of almost pure matter, and yet the Hawking radiation seems to return it as an even mix of matter/anti-matter.  This seems to violate some sort of balance between the two (which is already inexplicably imbalanced by the predominance of matter over antimatter).  Is there any sort of balance law that says that matter cannot be changed into antimatter without some sort of equal/opposite reaction?  If what you say is true, Hawking radiation seems to violate that balance law as it creates an even mix out of what was once mostly matter.  It feels wrong.
No such "balance law" exists.    For example, two gamma ray photons of sufficient energy can produce a electron-positron pair.  It doesn't matter what source generated those gamma ray photons.   
As far as the mass loss of the BH goes,   The BH gains mass by absorbing both "matter" and energy in the form of photons crossing the event horizon.  Once it crosses the event horizon, there is nothing that can distinguish what mass is due to energy and what is due to "matter" as far as anyone outside of the event horizon is concerned. We can't even know if such a distinction applies inside the event horizon.
Title: Re: How do black holes evaporate?
Post by: flummoxed on 17/04/2019 18:01:29
The energy books must be balanced in order for this particle to continue to exist, and this come from the mass of the BH.  One of the virtual particle pair has become a real particle at the expense of the BH.  This particle may escape, or more likely interact with another particle which produces light radiation that does escape the region near the event horizon

Am I correctly interpreting this. Both of the virtual particles carry on existing, the longer a virtual particle exists the more like a real particle it becomes. The energy to make them exist comes from the blackholes gravitational field which extends beyond the event horizon. The particle that escapes takes away gravitational energy and hence reduces the overall mass of the BH.


Title: Re: How do black holes evaporate?
Post by: Halc on 17/04/2019 20:33:51
No such "balance law" exists.    For example, two gamma ray photons of sufficient energy can produce a electron-positron pair.
But that's  an example of a balanced event.  Exactly equal amounts of matter and antimatter are generated by that, just as equal amounts are destroyed by the meeting of those two.
Yes, the gamma rays a neutral.  There isn't an anti-gamma ray, so the energy of them doesn't count as energy vs. anti-energy.  But matter in a black hole, if matter actually enters the black hole, seems to be neutral like that.  The merging of such a black hole and another would always produce a larger black hole, even if one of them was a black hole formed with antimatter.
It seems that if matter is actually prevented from crossing the event horizon, then there would be meaning to anti-black-hole and the merger of it  would perhaps do what?  Cancel??  That makes no sense because the total energy of the mutual annihilation would still leave that much mass's worth of energy sitting right there which still just makes for a bigger concentration of mass/energy.  No difference in other words.

I digress.  I was looking for an example of an imbalance event where matter is created or destroyed without respectively creating or destroying an equal amount of antimatter.

Quote
As far as the mass loss of the BH goes,   The BH gains mass by absorbing both "matter" and energy in the form of photons crossing the event horizon.
I get this, and it is a good argument against any balance.  There is only mass/energy at the end, and not matter/antimatter distinction.  BTW, I don't personally find it plausible that anything passes the event horizon if time dilation prevents it, but maybe quantum effects let this happen just like quantum effects permit Hawking radiation.  A unified theory would go a long way towards settling this debate.  I think Hawking himself found the 'nothing passes in' argument as a viable solution to the violation of conservation of information that seems to follow from the view that things actually fall past the event horizon.
Title: Re: How do black holes evaporate?
Post by: flummoxed on 18/04/2019 12:30:31
Black holes lose mass in more ways than Hawking radiation. Ligo detected a BH merger, three solar masses were lost in the form of gravitational waves.

The resultant BH was bigger. The event horizon would have become larger, so it would likely be spinning slower, but the impact may also have slowed the spin of the internal undefined stuff inside the resultant BH, causing it to lose energy via the gravitational wave. Is this a correct explanation. ?
Title: Re: How do black holes evaporate?
Post by: yor_on on 18/04/2019 21:51:26
Very comprehensive Janus. You define it as due to conservation laws which is pretty cool.
Title: Re: How do black holes evaporate?
Post by: evan_au on 18/04/2019 23:33:09
Quote from: Halc
I was looking for an example of an imbalance event where matter is created or destroyed without respectively creating or destroying an equal amount of antimatter.
A few Nobel Prizes have been awarded for discovering events that are not totally symmetric between matter and antimatter.
However, the degree of asymmetry is quite small in these scenarios, and these are not thought to be nearly strong enough to account for the total dominance of matter in out part of the universe (and the amount of matter in relation to the amount of photons).
See: https://en.wikipedia.org/wiki/CP_violation#Direct_CP_violation

Quote from: Hawking
the 'nothing passes in' argument
This is true from the view of distant observers, and does solve the information paradox for distant observers.
But from the viewpoint of someone falling into a black hole, there is no information paradox, and they do pass the location of the event horizon (from the viewpoint of a distant observer).

Quote from: flummoxed
but the impact (of 2 black holes) may also have slowed the spin of the internal undefined stuff inside the resultant BH
When black holes collide, their total angular momentum is conserved.
- Angular momentum is a vector - it has both direction and magnitude.

It is most likely that two black holes from different sources would have quite different directions and magnitudes of angular momentum.
- So when they collide, the angular momentum partially cancels out, resulting in an intermediate direction and a reduced magnitude
- In the extremely unlikely event that two black holes had equal and opposite angular momentum, and collided along their equators, you could end up with a non-spinning black hole.

Quote from: flummoxed
but the impact may also have slowed the spin of the internal undefined stuff inside the resultant BH, causing it to lose energy via the gravitational wave.
Radiation of gravitational energy is related to conservation of energy: Gravitational potential energy and gravitational waves.
- The gravitational waves convey information about the angular momentum of the black holes, but gravitational waves are not primarily caused by conservation of angular momentum.