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Author Topic: Is hawking radiation more to do with energy than mass?  (Read 3608 times)

Benjamin Main

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Benjamin Main  asked the Naked Scientists:
   
I was listening to the most recent episode of Naked Astronomy and in particular I noted Andrew Pontzen's response to the question from David Walker about whether there was a bias as to whether a particle or an antiparticle fell into a black hole in the particular depiction of Hawking radiation where such a pair of particles is produced around the event horizon.

Now, I am not a physicist, but it seems to me that Andrew's explanation was just plain wrong.  It seems to me that it does not matter whether the particle that escapes the black hole is a particle or an antiparticle...the black hole will lose mass equivalent to the energy of the particle emitted, so no bias in absorbing particles or antiparticles need exist.  The issue is not whether matter or antimatter falls into a black hole--in both cases, the black hole will grow by the mass of the object

I think that it's helpful to think of this in terms of the equivalency of matter and energy.  In this view, matter and antimatter are two different manifestations of energy that have the property of transforming into gamma radiation when corresponding particles of the two types (like a positron and an electron, a proton and an anti-proton, etc.) interact.  However, this interaction does not destroy the energy of the two particles.  Instead, it is emitted in the gamma radiation from the reaction.  As such, such an interaction occurring within the event horizon would have no effect as regardless of the form of the energy, it would continue on toward the singularity.

An antiparticle falling into a black hole makes the black hole more massive because antiparticles, just like their matter counterparts consist of a positive amount of energy.  So an antiparticle annihilating with a bit of matter falling into a black hole would not have any effect on the black hole's end mass--the gamma photon produced would still become a part of the black hole's mass, which is merely a manifestation of its energy.

So how does the conventional Hawking radiation explanation work?  In works on the properties of virtual particles, which come in and out of existence with no net change in energy.  In the case of Hawking radiation, a matter-antimatter pair form around the event horizon and one of the pair leaves the black hole's gravitational pull while the other falls in.  While it would seem that the one falling in would make the black hole larger, it must be remember that these particles came into being out of no energy and so the black hole ends up paying the "debt" of the particles' creation with its mass and this debt happens to be twice as large as the particle that fell in, as the other one escaped.

Ben Main
Neenah, WI, USA

What do you think?
« Last Edit: 06/02/2011 21:30:03 by _system »


 

Offline graham.d

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Is hawking radiation more to do with energy than mass?
« Reply #1 on: 07/02/2011 09:05:44 »
I don't know what was said on Naked Astronomy, but you have it about right in your last paragraph I think. It is sometimes difficult to explain this idea in simple terms, though.
 

Offline imatfaal

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Is hawking radiation more to do with energy than mass?
« Reply #2 on: 07/02/2011 12:27:24 »
Ben.  The problem is that the explanation in your final paragraph is a lovely explanation by Hawking (who had a great turn of phrase and way of making ideas come to life) - but it is only an illustration and not a trimmed down basis of the actual mechanism.

In Hawking's original paper he describes it as thus "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".  The actual mechanism is described in maths beyond my ken - but if you want to try  here is the original paper. 
 

Offline syhprum

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Is hawking radiation more to do with energy than mass?
« Reply #3 on: 07/02/2011 15:27:43 »
At the end of the paper Hawking puts forward some interesting ideas, refering to a Penrose diagram
"The horizontal line marked "singularity" is really a
region where the radius of curvature is of the order the Planck length. The matter
that runs into this region might reemerge in another universe or it might even
reemerge in our universe through the upper vertical line thus creating a naked
singularity of negative mass."
 

Offline yor_on

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Is hawking radiation more to do with energy than mass?
« Reply #4 on: 07/02/2011 19:05:51 »
"While it would seem that the one falling in would make the black hole larger, it must be remember that these particles came into being out of no energy and so the black hole ends up paying the "debt" of the particles' creation with its mass..

And this debt happens to be twice as large as the particle that fell in, as the other one escaped."

Some law of energy debt/conservation at play? Where it won't matter what we deem the in-falling particle to have for sign? So, assuming that particles exist on their own, and also can annihilate each other when of different signs. It still won't matter the sign of the in-falling one as there is a 'hidden law of conservation' between a singularity and our universe?

I'm losing you there Benjamin. It may be okay to assume such a law, although it's new to me, but where else do we see it?

A singularity is not defined as being 'in touch'. Its 'time cone' point only one way, into the center of that black hole. Any 'radiation' coming from it must be defined as having no 'communication' or the idea that a Black hole' is a singularity loses its meaning.

The idea of describing it as the 'anti particle' being the one 'surviving' long enough to decrease a Black Holes mass inside its EV at the same time as the 'pair productions' twin survive inside our universe makes sense to me, in that it doesn't really 'communicate' being entangled. Your assumption seems on the other hand to assume a communication of sorts? As well as being a 'constant' of sorts if so, although not proven as I know it?

Anyone that can describe where we see it elsewhere?
 

Offline Meng Bomin

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Is hawking radiation more to do with energy than mass?
« Reply #5 on: 11/02/2011 07:53:55 »
First let me identify myself as Benjamin Main, the original submitter.  I want to thank imatfaal in particular for posting the original paper.  I myself do not currently have the skills to make sense of much of the paper, not having had a proper training in the physics or accompanying mathematics that Hawking uses, though I hope to acquire some of the skills in my free time eventually.

That eventuality will not be soon enough for me to reply in a reasonable amount of time, so I'm going to have to rely on the illustrative language of Hawking's paper rather than the more precise mathematical elements.  It seemed to me that the relevant illustrative language was here:

Quote
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. It should not be thought unreasonable that a black hole, which is an excited state of the gravitational field, should decay quantum mechanically and that, because of quantum fluctuation of the metric, energy should be able to tunnel out of the potential well of a black hole. This particle creation is directly analogous to that caused by a deep potential well in flat space-time [18]. The real justification of the thermal emission is the mathematical derivation given in Section (2) for the case of an uncharged non-rotating black hole. The effects of angular momentum and charge are considered in Section (3). In Section (4) it is shown that any renormalization of the energymomentum tensor with suitable properties must give a negative energy flow down the black hole and consequent decrease in the area of the event horizon.
This negative energy flow is non-observable locally.

This is a pretty long and fairly technical bit of writing in itself, but I think I can muster through in restating my concern in light of this part of the paper as well as restating the picture I had in my head as I wrote in the original email that is the opening post of this thread.

Part of the problem I had with the description by Andrew Pontzen and the similar one given by yor_on is the use of "anti-particle" in place of "negative energy particle" that is used by Hawking in the above vignette because "anti-particle" implies an antimatter particle (such as a positron), which is actually a positive energy particle.  So if you were to send in an antiparticle, you would still increase the energy of the black hole, which in the type of language used by Hawking above, would increase the area of the event horizon.  Antimatter may have the opposite charge to its matter counterparts and they may mutually annihilate upon interaction, but the result is the release of energy in the form of gamma radiation.  So, in the end, an antimatter particle would not affect a black hole any differently that

So the vignette I had in my head (and this may well have been derived from content of a previous Naked Astronomy podcast) was that you had a virtual particle-antiparticle pair arise near the event horizon and that while normally, such a pair would annihilate with no net energy change, if one of the pair crossed the event horizon and the other escaped the black hole's gravity well, there would be one real escaped particle and one real particle that was consumed by the black hole.  The end result would again have to have no net change in energy, but since a particle escaped (and thus an amount of positive energy), there is energy lost by the black hole.

Now clearly, there are some differences between this vignette and the one described by Hawking, as rather than positing a particle-antiparticle pair, he posits a negative energy particle that tunnels across the event horizon with the positive energy particle escaping.  Obviously, a negative energy particle would more concretely satisfy the condition of a negative energy flux across the event horizon than the scenario I described where there is an "energy debt" that arises from the creation of two positive energy virtual particles, one of which escapes.

Ultimately, as both Hawking and imatfaal point out, the actual mechanics of Hawking radiation are best described mathematically (and unfortunately in terms with which I am not yet familiar), so these vignettes are perhaps limited in their descriptive characteristics and maybe fixating on the details of  what's ultimately an imprecise way of translating a more complicated and technical description into something intuitive to laymen such as myself is akin to asking how many angels can dance on the head of a pin.
 

Offline yor_on

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Is hawking radiation more to do with energy than mass?
« Reply #6 on: 12/02/2011 18:14:41 »
Okay, here's one take on it. Assume that you have virtual pair getting produced at the EV, one wandering in the other being outside. Assume that the one wandering in is the positive part of the particle-pair, with the anti particle being outside. The anti particle wandering away will have a mass too, now subtracting it from the black hole as it annihilates. Subtracting as all 'energy' only can have one direction, into the Black Hole at the EV. The positive particle left inside is just half of the original mass existing from the beginning. Turn it around and you will have a negative particle annihilating inside the EV taking itself out. What it builds on, as I see it, is the assumption of those 'virtual pair-productions' being directly coupled to the Black Holes 'Energy' if you like.

That assumption seems quite reasonable. Then we have the idea of tunneling too. It's another way particles might leave a Black Hole. It took me some time to turn my head around this idea, or rather, the explanations for how it was thought to work were not that good really :) But I hope this make sense.
==

What one might question is the idea of this anti particle wandering really bring any energy inside our side of 'SpaceTime'? Especially if it annihilates meeting a particle, I doubt the positive rest will be bigger than the particle annihilated by our 'anti particle', so? But it's an alternative way of describing it, even though it will become difficult to refer to it as a 'energy debt' if so. That as the 'anti particle' actually eat on us as well as on the Black Hole, if you see how I think.
==

And so we get to my original argument, that I see it as a 'Singularity' from where no useful 'information' can be extracted. Does that one still hold if Hawking radiation works like this? Yes, I think it do. If someone have another view you better give me a example of how to extract information from that radiation.
==

What one might notice here is that even though the Black hole, looked at this way, 'evaporates' it will do it slower when getting a positive particle, faster with a negative particle as that one might be assumed to also take out a positive but both particles leaving a positive residue. so looked at as a 'energy debt' there is a uneven distribution, or none at all in case of it being a 'anti particle' coming to exist inside SpaceTime. But that is also a factor of what 'time scale' you choose. you might argue that in 'time' all of the energy will have worked its way out from that Black Hole, even though our universe then should have ''stopped' the only new usable 'energy' being the one coming from the Black Hole.

Ah well, maybe?
==

Rereading you, no having a anti particle particle annihilation is supposed to leave a positive rest, but the 'mass' getting annihilated will still be greater than the rest/residue left. It's just the difference between them taking each other out perfectly, or leaving some slight positive 'energy'. But if they do, that has to be included too.
« Last Edit: 12/02/2011 19:28:56 by yor_on »
 

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Is hawking radiation more to do with energy than mass?
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