hawking radiation question

[hoola]

I have read accounts of the separation of virtual particles at the event horizon with the anti-matter particle falling into the hole, and the matter particle escaping, forming the radiation and allowing a net loss to the BH. Why does the reverse not happen as frequently with the anti-matter escaping into space and the matter particle falling into the BH, with the effect of increasing black hole mass? I had presumed the energy loss to the black hole was the "work done" to separate the particles, and the infalling number of anti-matter and matter particles would average out numerically in a cancellation effect. Plus, I read that region bounded by the inside the event horizon and the singularity is a vacuum. Does this mean that this area is "cleansed" of the spontaneous appearance of virtual particles as a sort of forbidden region?

[Sorcerer]

Very good point.

Ok, so I probably know as much if not less about this than you but, I am guessing the slight difference between the ratio of matter and antimatter is due to their CP symmetry. But that's just a guess.

Perhaps it is only probability that a black hole can evaporate, it's just as likely that it will continue to grow. It's like a VP pair is a toss of a coin and since each "roll" is independant, over time it is possible for enough mass to escape for the BH to no longer form an event horizon.

And my last guess would be, the mass/energy needed for the existence of the VP pair is borrowed from the black hole. Thus even if an antimatter particle escaped and a matter particle entered the BH, half of that borrowed mass/energy would still be lost. As the antimatter particle drifts off and annihilates ( or even if it doesn't ) with a matter particle away from the event horizon, the result is a net loss to the black hole.

From the wiki "Physical insight into the process may be gained by imagining that particle-antiparticle radiation is emitted from just beyond the event horizon. This radiation does not come directly from the black hole itself, but rather is a result of virtual particles being "boosted" by the black hole's gravitation into becoming real particles.^[11] As the particle-antiparticle pair was produced by the black hole's gravitational energy, the escape of one of the particles takes away some of the mass of the black hole.^[12]"

Which is the simple version and it alludes to the black holes gravitational energy and therefore mass being used to create the VP pair. So I guess my #3 was the most correct.

Edited February 21, 2015 by Sorcerer

[hoola]

Thank you scorcerer, the cp symmetry I presume to be applicable to the overall ratio of matter/antimatter of the total universe, and I am specifically addressing virtual particles, which I presume are precisely half matter, half anti-matter. As far as the particles borrowing energy at the black hole, the particles appear everywhere, and not at only at horizons. My second question involved the supposed vacuum within the black hole, between the horizon and the singularity. Is that a normal vacuum with virtual particles, or one truly devoid of these items? If the vacuum is to be called a "super" vacuum, that is without the normal space vacuum particles, that calls into mind the sharnhorst effect, which posits that C is slightly higher if the virtual particles were somehow removed from normal space. Could a slightly higher C within the hole affect overall system behavior?

Edited February 21, 2015 by hoola

[ajb]

Why would it make any difference is a particle or anti-particle was to fall in? The escaping particle or anti-particle takes some of the black holes mass to become real. (Heuristically speaking here. )

[Strange]

I have read accounts of the separation of virtual particles at the event horizon with the anti-matter particle falling into the hole, and the matter particle escaping, forming the radiation and allowing a net loss to the BH.

 

Either particle can fall into the black hole.

 

Note that this analogy comes from Hawking himself, but I don't think it is a completely realistic description of what the maths describes (but the maths is totally beyond me, anyway).

 

Anyway, the idea is that the gravitational field of the black hole provides the energy to create a pair of particles - this is equivalent to the mass of two particles. One of the particles then falls through the event horizon contributing its mass back to the black hole. The other escapes taking its mass/energy away. So the black hole loses the net mass of one particle.

[ajb]

Note that this analogy comes from Hawking himself, but I don't think it is a completely realistic description of what the maths describes (but the maths is totally beyond me, anyway).

The original calculation is based on a very important 'difficulty' with quantum field theory on a curved space-time. That is different observers will not agree on the vacuum. This is the true origin of Hawking radiation; one man's empty state is another man's filled state! An observer hovering just above the horizon will see something different that an external observer at infinity. This is due to the fact that the observer near the horizon needs to keep accelerating just to maintain his position. The Unruh effect states that an accelerating observer will observe black body radiation while an inertial one will see none. Thus, the Unruh effect and Hawking radiation are deeply tied. (Both effects were predicted independently at about the same time)

 

Only later was the originally heuristic picture of particle and anti-particle pairs with one falling in shown to be a reasonable way to picture the process. It was Parikh and Wilczek who showed that tunnelling can be used to explain Hawking radiation. I forget the year, but a quick search of the arXiv will give you the paper.

[Strange]

Thanks ajb. That first paragraph is the explanation I have read before. I wasn't aware that the particle-antiparticle model had been formalised.

The paper is here, for anyone else interested: http://arxiv.org/abs/hep-th/9907001

(I don't claim to fully understand it, but there are some interesting points made.)

[ajb]

I am glad that I have, in some small way, helped.

[hoola]

I would seem the BH loses mass independent of whether the escaping particle is matter or anti-matter. Since the ratio should be equal with additive and subtractive particle elements escaping, isn't the real loss to the BH the work done to separate them, and not the fact that one escapes? Given the scenario that upon separation, and one falls in immediately, then the other one gets deflected somehow, and it goes into the hole also, would there be some loss to BH mass, as the particles have been separated, but will not recombine to it's original partner within the hole, or would the energy loss to separate them be gained back in equal measure since both eventually are inside the hole? My question regarding the parameters of the "vacuum" within the hole has not been addressed...namely, can virtual particle pairs appear within the hole, as they do at the horizon and beyond?

[Strange]

Given the scenario that upon separation, and one falls in immediately, then the other one gets deflected somehow, and it goes into the hole also, would there be some loss to BH mass, as the particles have been separated, but will not recombine to it's original partner within the hole, or would the energy loss to separate them be gained back in equal measure since both eventually are inside the hole?

 

Energy conservation still applies, so I can't see any reason why the full energy would not be returned to the black hole. (Although I have learned not to take anything for granted when it comes to black holes.)

 

My question regarding the parameters of the "vacuum" within the hole has not been addressed...namely, can virtual particle pairs appear within the hole, as they do at the horizon and beyond?

 

This vacuum state (which I think is only apparent to an observer freefalling through the event horizon - because they do not see Hawking radiation) is the lowest energy state containg no physical particles. But this is a non-zero energy state so virtual particles are still present.

https://en.wikipedia.org/wiki/Vacuum_state

Edited February 21, 2015 by Strange

[hoola]

wouldn't these particles be ripped apart in a similar fashion as the ones appearing at the horizon as they plummet into the singularity? Wouldn't these separated particles gain mass as they accelerate further past the horizon, at least in the case of small BHs?

[MigL]

How would an elementary virtual particle get ripped apart ? What would be the resultant constituents ?

 

The reason objects get 'ripped apart' when they cross the event horizon is due to tidal forces. In effect, for small black holes or when approaching the center ( singularity ? ), the gravity differential between the object's feet and head is soooo large that 'spaghettification' results. An elementary particle like an electron or a quark, is thought to be ( very close to ) dimensionless.

So where is the gravitational differential ???

 

And why would they gain mass as 'they accelerate further past the horizon'.

[hoola]

the resultant constituents would be the mathematical description of these supposed "fundamental" particles...although this is veering into speculation and in the incorrect forum. They would accelerate all the way from outside the horizon, to the singularity itself, and become the center itself, since it has no dimensions with which to maintain any distinct entities...again, speculation..but what I meant by "ripped apart" was individual elements of the pair being "ripped apart" by the tidal forces into separate particles, (then reduced into a non material description of the high mass singularity.) You were thinking past where I wanted to go in this forum...

[Strange]

It doesn't really matter what happens beyond the event horizon as all we can ever hope to know is the mass (and charge and angular momentum) of the black hole. They could turn into singing chocolate penguins, for all we know. Perhaps a theory of quantum gravity would tell us more.

[hoola]

strange, in response to entry #5 wherin you state that the energy of the black hole creates the particles, the particles appear everywhere, right? It is only at a gravity well of sufficient strength that separates them , ...ps, I don't know why this got underlined...not deliberate...darn, still underlined...anyway doesn't the casimir effect show that they are everywhere, and in higher numbers wherin baryonic matter density is lower?

Edited February 22, 2015 by hoola

[Strange]

Specifically, it is (from what I understand) the presence of the event horizon that separates them. In the case that the particle pair are created just inside the event horizon, then one of them is allowed to tunnel out. The Parikh and Wilczek paper seems to say that the only reason it can tunnel out it because the event horizon shrinks due to the loss of mass. (A similar argument applies to pairs formed just outside the event horizon.)

[hoola]

very interesting, thank you strange...this sounds like the "evaporative" effect mechanism that shrinks them down, is that correct?

Edited February 22, 2015 by hoola

[Strange]

very interesting, thank you strange...this sounds like the "evaporative" effect mechanism that shrinks them down, is that correct?

 

Exactly.