What are the limitations of the heuristic picture of Hawking radiation?

[Allen_Wolf]

What happens to the energy that goes inside a black hole. Will it stay there or get converted into some other forms of energy. What will happen to it?

 

[newjerseyrunner]

It get's stuck, that's the point of a black hole, anything that gets sucked down into it never comes out.

That was the short answer. The more complex answer is that it's energy will constantly create particle/antiparticle pairs (like everything else) which will almost instantly destroy each other. Every once in a while though, those particles are created in exactly the right point beyond the event horizon that one of them escapes. This is called Hawking Radiation, and it will eventually cause all black holes to evaporate. The largest black holes (which evaporate most slowly) will finally pop out of existence in around 10^100 years.

 

[Chalnoth]

What happens to the energy that goes inside a black hole. Will it stay there or get converted into some other forms of energy. What will happen to it?

It becomes added to the mass of the black hole.

As for what precisely occurs on the interior of a black hole, that is currently unknown. Presumably it depends upon the details of quantum gravity, which we don't yet have a well-tested theory for.

 

[Allen_Wolf]

So will light energy also get added to the mass of the black hole?

 

[Allen_Wolf]

It get's stuck, that's the point of a black hole, anything that gets sucked down into it never comes out.

That was the short answer. The more complex answer is that it's energy will constantly create particle/antiparticle pairs (like everything else) which will almost instantly destroy each other. Every once in a while though, those particles are created in exactly the right point beyond the event horizon that one of them escapes. This is called Hawking Radiation, and it will eventually cause all black holes to evaporate. The largest black holes (which evaporate most slowly) will finally pop out of existence in around 10^100 years.

So won't the mass be balanced by the antiparticles?

 

[Chalnoth]

So won't the mass be balanced by the antiparticles?

No. Anti-particles have positive mass, just like particles.

Doesn't matter what particles fall into the black hole, whether photons, electrons, positrons, or anything else, they all add their energy to the black hole's mass.

 

[PeterDonis]

won't the mass be balanced by the antiparticles?

No. In the heuristic model of Hawking radiation that newjerseyrunner described, the antiparticle that falls into the hole (while its particle partner escapes) has negative energy, so "adding" it to the hole's mass results in a slightly reduced mass for the hole. Note that this is a heuristic model and has many limitations.

Anti-particles have positive mass, just like particles.

Not in the particular case newjerseyrunner was describing--see above. But one of the obvious limitations of this heuristic is trying to explain how a particle or antiparticle can have negative energy--you end up having to unpack "negative energy" into something that doesn't really justify that ordinary language phrase.

 

[Allen_Wolf]

No. Anti-particles have positive mass, just like particles.

Sir I'm still a bit confused.
The particles that go into the black hole also has +ve mass right?

 

[Allen_Wolf]

No. In the heuristic model of Hawking radiation that newjerseyrunner described, the antiparticle that falls into the hole (while its particle partner escapes) has negative energy, so "adding" it to the hole's mass results in a slightly reduced mass for the hole. Note that this is a heuristic model and has many limitations.
Not in the particular case newjerseyrunner was describing--see above. But one of the obvious limitations of this heuristic is trying to explain how a particle or antiparticle can have negative energy--you end up having to unpack "negative energy" into something that doesn't really justify that ordinary language phrase.

Thank you SIr

 

[newjerseyrunner]

So will light energy also get added to the mass of the black hole?

Yes, in such extremes of the universe, it's important to remember that matter is sort of like congealed energy, and when talking about gravity, energy and mass are the same and interchangeable.

 

[PeterDonis]

The particles that go into the black hole also has +ve mass right?

Just to make sure it's clear, there are two different possible cases.

In the case of an ordinary particle or antiparticle falling into a black hole, both have positive mass.

In the case of Hawking radiation, in the heuristic model newjerseyrunner described, a particle-antiparticle pair pops out of the vacuum just outside the horizon of the hole. One of the pair falls into the hole while the other pair escapes. The one that escapes has positive energy; the one that falls in has negative energy. The net effect is that a small bit of the hole's mass is transferred to the escaping particle, and the hole's mass is correspondingly reduced.

 

[Allen_Wolf]

Just one more doubt sir. Why and how does only the +ve matter escape ?
I mean the particle

 

[newjerseyrunner]

You'll kick yourself when you realize why, it's nothing special or tricky, just geometry.

If only one of the particles gets kicked out and the other falls back into the hole, that means that they had different gravitational potentials. Therefore the one created further from the black hole must have more energy than the one below it. Since the creation of the pair can basically be described as them borrowing energy from spacetime, that energy debt has to be repaid, normally it happens through recombination, this time, it has to end up as a net loss of energy for the black hole.

 

[Allen_Wolf]

You'll kick yourself when you realize why, it's nothing special or tricky, just geometry.

If only one of the particles gets kicked out and the other falls back into the hole, that means that they had different gravitational potentials. Therefore the one created further from the black hole must have more energy than the one below it. Since the creation of the pair can basically be described as them borrowing energy from spacetime, that energy debt has to be repaid, normally it happens through recombination, this time, it has to end up as a net loss of energy for the black hole.

thank you sir

 

[PeterDonis]

Why and how does only the +ve matter escape ?

Again, please bear in mind that this is a heuristic model and has many limitations. You should not expect it to make complete sense, because the actual physics is not this heuristic model, it's the underlying quantum field theory.

That said, the answer to your question, in the heuristic model, is that the "negative energy" particle can't exist outside the hole's horizon; only "positive energy" particles can exist there. So the particle that escapes has to have positive energy.

 

[PeterDonis]

If only one of the particles gets kicked out and the other falls back into the hole, that means that they had different gravitational potentials.

No, it doesn't. This is an incorrect extension of the heuristic model. Gravitational potential has nothing to do with the process of Hawking radiation. You can model the process, at this heuristic level, with both particles being created at exactly the same altitude above the horizon, and therefore at exactly the same gravitational potential; so it can't possibly be a difference in potential that makes one fall into the hole and the other escape.

 

[Allen_Wolf]

No, it doesn't. This is an incorrect extension of the heuristic model. Gravitational potential has nothing to do with the process of Hawking radiation. You can model the process, at this heuristic level, with both particles being created at exactly the same altitude above the horizon, and therefore at exactly the same gravitational potential; so it can't possibly be a difference in potential that makes one fall into the hole and the other escape.

Thank you for the correction

 

[newjerseyrunner]

No, it doesn't. This is an incorrect extension of the heuristic model. Gravitational potential has nothing to do with the process of Hawking radiation. You can model the process, at this heuristic level, with both particles being created at exactly the same altitude above the horizon, and therefore at exactly the same gravitational potential; so it can't possibly be a difference in potential that makes one fall into the hole and the other escape.

Interesting, so what causes one particle to fall in and the other to be ejected? Are they created identically then quantum fluctuations separate them or something?

 

[PeterDonis]

Are they created identically then quantum fluctuations separate them or something?

Sort of, yes. Once more, remember that this is a heuristic model. In the heuristic model, the particles are created at the same point of spacetime, but with slightly different radial velocities--one is moving a bit inward, the other a bit outward. (They are moving at the same speed, because their net energy and momentum is zero, but different directions.) Then the hole's tidal gravity separates them further, to the point that one particle, the one that ends up with negative energy, falls below the horizon while the other one flies outward and ends up with positive energy and escapes.

 

[Stephanus]

...The more complex answer is that it's energy will constantly create particle/antiparticle pairs (like everything else) which will almost instantly destroy each other. Every once in a while though, those particles are created in exactly the right point beyond the event horizon that one of them escapes. This is called Hawking Radiation, and it will eventually cause all black holes to evaporate. The largest black holes (which evaporate most slowly) will finally pop out of existence in around 10^100 years.

Oh, that's Hawking Radiation? All this time I was wondering, that anything (this 'radiation) can escape black hole.
So this particle created just outside event horizon.
What particle is it?
Even in the event horizon it takes near the speed of light to escape black hole, so there's a chance that the particle gets attracted into the black hole instead of escaping?
Now about its speed. Once this particle is created it has already tremendous speed?

And last question.
Perhaps this is off topic.
There are particles/anti particles created near the event horizon, why?
Why is energy converted near EH?
Does it happen in our everyday life? Not in MRI machine I mean.
I mean in our stove, refrigerator, does particle/antiparticle pair is created from energy in our everyday life?
And if it's not, just like my question above, why black hole creates particle/anti particle?

Thank you very much.

 

[newjerseyrunner]

Oh, that's Hawking Radiation? All this time I was wondering, that anything (this 'radiation) can escape black hole.
So this particle created just outside event horizon.
What particle is it?
Even in the event horizon it takes near the speed of light to escape black hole, so there's a chance that the particle gets attracted into the black hole instead of escaping?
Now about its speed. Once this particle is created it has already tremendous speed?

And last question.
Perhaps this is off topic.
There are particles/anti particles created near the event horizon, why?
Why is energy converted near EH?
Does it happen in our everyday life? Not in MRI machine I mean.
I mean in our stove, refrigerator, does particle/antiparticle pair is created from energy in our everyday life?
And if it's not, just like my question above, why black hole creates particle/anti particle?

Thank you very much.

Black holes are not special, and particle pair production is not a properly of them. It seems to be a property of spacetime itself, it happens all the time, everywhere.

I'm pretty sure that the particle itself is either an electron or a positron.

 

[Frimus]

As for Hawking radiation and its localization I recommend Sabine Hossenfelder's article on her blog: Hawking radiation is not produced at the black hole horizon

 

[Stephanus]

Black holes are not special, and particle pair production is not a properly of them. It seems to be a property of spacetime itself, it happens all the time, everywhere.

I'm pretty sure that the particle itself is either an electron or a positron.

Do you mean that everytime, anywhere not just in MRI machine, electron/positron production can happen? In my kitchen for example?

 

[PeterDonis]

I'm pretty sure that the particle itself is either an electron or a positron.

No, it can't be, at least not for a black hole that is electrically neutral. Only a neutral particle can be emitted. But any neutral particle is possible (though neutral particles with greater rest mass are less likely).

Do you mean that everytime, anywhere not just in MRI machine, electron/positron production can happen? In my kitchen for example?

Not only can it happen, it is happening--at least, it is if you interpret "vacuum fluctuations" as virtual particles. But that interpretation has significant limitations.

 

[Stephanus]

...Not only can it happen, it is happening--at least, it is if you interpret "vacuum fluctuations" as virtual particles. But that interpretation has significant limitations.

Sorry PeterDonis, so you're saying that everytime anywhere (I don't know the rate) there are particle/anti particle created?
And if it takes place near the EH, then the outer particle is thrown away decreasing this black hole mass?
I have other questions, too. But I'll wait for the answer.

Thanks.

 

[PeterDonis]

so you're saying that everytime anywhere (I don't know the rate) there are particle/anti particle created?

I'm saying that that is one (limited) interpretation of the fact that, in quantum field theory, the vacuum has nonzero energy. But it's not the only possible interpretation.

Also, under this interpretation, the particle/antiparticle pairs that are continually being created everywhere annihilate each other right after they are created. They don't interact with anything else.

 

[Stephanus]

...Also, under this interpretation, the particle/antiparticle pairs that are continually being created everywhere annihilate each other right after...

So in this case of Hawking Radiation, there are particle/antiparticle paris that are created right at the Event Horizon, and the other gets propelled away from black hole, and the other gets sucked into black hole?
And what about the "get away" speed? Is it near the speed of light?

Thank you

 

[PeterDonis]

in this case of Hawking Radiation, there are particle/antiparticle paris that are created right at the Event Horizon, and the other gets propelled away from black hole, and the other gets sucked into black hole?

In a particular heuristic picture of Hawking radiation, yes. But, as I've said, this heuristic picture has significant limitations.

what about the "get away" speed? Is it near the speed of light?

In that particular heuristic picture, yes, the particle that flies away from the hole is moving at nearly the speed of light, relative to observers that are "hovering" near the hole's horizon. But, once more, this heuristic picture has significant limitations.

 

[Stephanus]

So in this case of Hawking Radiation, there are particle/antiparticle paris that are created right at the Event Horizon? , and the other gets propelled away from black hole, and the other gets sucked into black hole?

In a particular heuristic picture of Hawking radiation, yes. But, as I've said, this heuristic picture has significant limitations.

Thank you

And what about the "get away" speed? Is it near the speed of light?

In that particular heuristic picture, yes, the particle that flies away from the hole is moving at nearly the speed of light, relative to observers that are "hovering" near the hole's horizon. But, once more, this heuristic picture has significant limitations.

Thank you

What limitations? But perhaps that's for another time.
This is good for me
Thanks