Why is Hawking Radiation Unequal for Matter & Antimatter?

[Pouya Pourkarim]

we say everytime a couple of matter-antimatter particles get born near the edge of a black hole one of them falls into it and the other one escapes.
And we everytime mention that the antimatter particle kind of eats a bit of black holes mass out...and by time the black hole gets smaller and smaller and say evaporates...
And the pile of scaped particles is what we call the Hawking radiation (?!)
Here is the question:
How come the chanse of falling into the black hole or scaping it isn’t statistically the same for matter and antimatter particles?

 

[Orodruin]

we say everytime a couple of matter-antimatter particles get born near the edge of a black hole one of them falls into it and the other one escapes.

This is a heavily popularised description of what goes on (as stated by Hawking himself, it was just the closest popular analogy he could think of). You should not use it too much to try to understand things.

And we everytime mention that the antimatter particle kind of eats a bit of black holes mass out...

This is not even true in the analogy. In the analogy one of them (particle or antiparticle) will have negative energy and be absorbed. This is what decreases the BH mass.

How come the chanse of falling into the black hole or scaping it isn’t statistically the same for matter and antimatter particles?

It is. Hence your questionis based on a false premise.

 

[Nugatory]

We say everytime a couple of matter-antimatter particles get born near the edge of a black hole one of them falls into it and the other one escapes.

We say that, but as @Orodruin points out above, that's not what's really going on.
You might take a look at Hawking's original paper if only to see why the simplified description is so popular, and you will find a much more user-friendly explanation here: http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html

 

[sweet springs]

It is. Hence your questionis based on a false premise.

Dose the same chance for matter and antimatter means that we may use BH radiation as a good source of antimatter that scarcely exist in our universe ?

 

[Orodruin]

Dose the same chance for matter and antimatter means that we may use BH radiation as a good source of antimatter that scarcely exist in our universe ?

No.

 

[stevendaryl]

I've always been fascinated by Hawking's layman's explanation for Hawking radiation in terms of virtual particles. There are similar "virtual particle" or "vacuum fluctuation" explanations for a number of phenomena, including the Casimir effect. I understand very well that these explanations have no physical meaning, because virtual particles and vacuum fluctuations are just reifications of terms appearing in a power series expansion. I do wonder, though, whether there might be a way to make this kind of hand-wavy reasoning rigorous.

 

[ISTHISNAMEGONE]

I also have a very similar problem with this theory.

If it isn't a 50/50 chance that the particle with negative energy falls into the black hole then what governs that?

 

[phinds]

If it isn't a 50/50 chance that the particle with negative energy falls into the black hole then what governs that?

As Hawking himself has said, you can't really explain that in English, you have to go to the math, were it is clear. As stated above in this thread, your question is based on a false premise.

 

[ISTHISNAMEGONE]

Okay so the false premise is the fact it falls into the black hole? or the fact that I'm even considering it as a percentage?

I know i could look at the mathematics but that's why I came to this forum, to talk to people who already know the math. But if it is necessary I can take a look.

 

[Orodruin]

Okay so the false premise is the fact it falls into the black hole? or the fact that I'm even considering it as a percentage?

The fact that you are even considering it as a particle-antiparticle pair.

 

[phinds]

Okay so the false premise is the fact it falls into the black hole? or the fact that I'm even considering it as a percentage?

from the original paper on what is now called Hawking Radiation:

As the mass of the black hole decreased, the area of the event horizon would
have to go down, thus violating the law that, classically, the area cannot decrease
[7, 12]. This violation must, presumably, be caused by a flux of negative energy
across the event horizon which balances the positive energy flux emitted to
infinity. One might picture this negative energy flux in the following way. Just
outside the event horizon there will be virtual pairs of particles, one with negative
energy and one with positive energy. The negative particle is in a region which
is classically forbidden but it can tunnel through the event horizon to the region
inside the black hole where the Killing vector which represents time translations
is spacelike. In this region the particle can exist as a real particle with a timelike
momentum vector even though its energy relative to infinity as measured by the
time translation Killing vector is negative. The other particle of the pair, having
a positive energy, can escape to infinity where it constitutes a part of the thermal
emission described above. The probability of the negative energy particle tunnelling
through the horizon is governed by the surface gravity K since this quantity
measures the gradient of the magnitude of the Killing vector or, in other words,
how fast the Killing vector is becoming spacelike. Instead of thinking of negative
energy particles tunnelling through the horizon in the positive sense of time one
could regard them as positive energy particles crossing the horizon on pastdirected
world-lines and then being scattered on to future-directed world-lines by
the gravitational field. It should be emphasized that these pictures of the mechanism
responsible for the thermal emission and area decrease are heuristic only
and should not be taken too literally.

 

[Nugatory]

Okay so the false premise is the fact it falls into the black hole? or the fact that I'm even considering it as a percentage?

I know i could look at the mathematics but that's why I came to this forum, to talk to people who already know the math. But if it is necessary I can take a look.

You might try this link: http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html

Hawking's paper (not sure if it's the same one @phinds quoted) is https://projecteuclid.org/download/pdf_1/euclid.cmp/1103899181

 

[ISTHISNAMEGONE]

Thank you for all your responses.

I recently went to a talk on Einstein-Rosen bridges which may have confused my understanding of this phenomena even more. Because I was imagining a linked pair of... something at the edge of a black hole and collapsing this bridge gave rise to this specific phenomena, or the ideas were linked in some way.

But I think after having a quick look at the paper I have to admit I would need to spend a decent amount of time brushing up on my mathematical skills before I could even consider this phenomena properly.

Thanks for all your help!