# Hawkin Radiation and Evaporating Black Holes



## mosaix (May 8, 2013)

I'd never really understood this. I couldn't understand how a black hole gaining a particle caused it to evaporate.

In *New Scientist, 27th April, page 34,* there's the following letter:

_From Thor Simpson, Oxted, Surrey, UK.
Your look at the black hole firewall paradox described Hawkin radiation as the escape of one of a pair of virtual particles that pop into existence at the event horizon while the other falls into the black hole (6 April p38). So how does this radiation diminish the black hole if, for each particle radiated, one is captured?_

The editor replies:_

The particle that is captured by the black hole has negative energy. Much as the black hole's mass increases when anything with positive energy falls into it, its mass decreases when a particle with negative energy falls in. The upshot is the back hole slowly evaporates. _


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## thaddeus6th (May 8, 2013)

Not a science chap, but that sounds odd to me as well. Negative energy appears to equal negative mass...

Mind you, this level of science is well above me.


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## Foxbat (May 8, 2013)

I think we need to remember what mass is in physics terms - IIRC- the measure of inertia of a particle, and therefore ability of an object to resist  a change in momentum. 

I'm only guessing but perhaps the negative mass referred to is a particle with inertia that is opposite to the norm (something like matter/antimatter). This may explain the concept of negative mass.


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## Venusian Broon (May 8, 2013)

My understanding of these things is pretty limited, but I believe when they discuss virtual particles, these are weird transitory states that arise out of the mathematics of perturbations (or pictorally the things in Feynman Diagrams). And that these beasts can be really quite different to real particles. 

However it is assumed that when virtual particles pop into existence that they still obey some of the real basic conservation laws - so total fermion number of the universe must be conserved (or put another way if a fermion pops up, say an electron, it's anti-matter opposite must pop up too). Also the real big daddy of conservation laws - energy cannot be created or destroyed - holds.

As for Hawking radiation, the particles they are talking about are photons (or at least when the escaping particle becomes 'real' it's a photon...I think). Thus when a virtual photon pops into existence right at the event horizon, to balance the sudden appearence of a photon and to conserve energy a virtual anti-photon* has to appear which must have equal but negative energy. 

For some reason that is beyond me to explain**, it's the negative energy virtual photon that gets captures, and thus again, to satisfy the conservation of energy, the total energy of the black hole must go down.

Again, as Astrophysics was never a field I studied, for some reason decreasing the energy of a black hole makes it shrink. I unfortunately can't adequately explain - perhaps delta E = delta mc^2...but I think it's a bit more complicated than that and requires applying the second law of thermodynamics and entropy...**

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* Or a great number of them perhaps - I don't think you need to conserve total boson numbers in this case, just the total energy of the virtual system must be zero.

**i.e. its getting late and my brain is already deep fried


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## Ursa major (May 9, 2013)

Venusian Broon said:


> Again, as Astrophysics was never a field I studied, for some reason decreasing the energy of a black hole makes it shrink. I unfortunately can't adequately explain - perhaps delta E = delta mc^2...but I think it's a bit more complicated than that and requires applying the second law of thermodynamics and entropy.


It's late, but my brain can be fried at any time of day. 


Whether it represents the theory/hypotheses/conjectures of real scientists or not (I'm guessing not, with a capital N), my brain seems to latch onto the idea that it's the surface area (as apparent to the universe at large) of a black hole that's affected by its apparent mass, as if a given area of space (spacetime?) can only cope with the transmission of a certain maximum value of gravitational pull** and no more, so that where the pull becomes greater, the apparent surface area must increase to match this, and where it reduces, the surface area can shrink.

A consequence of this could be that the actual mass (serious handwaving in progress) of a black hole could be greater than that which can be expressed, given the black hole's apparent surface area.

I'm confident that this idea and any possible consequences  of it have no validity at all**, but it helps me think about it.


** - After all, the modest mass of, say, a cat, doesn't cause the cat's apparent surface area to be something we can't see even with the most powerful microscope.


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## Foxbat (May 9, 2013)

> As for Hawking radiation, the particles they are talking about are photons (or at least when the escaping particle becomes 'real' it's a photon...I think). Thus when a virtual photon pops into existence right at the event horizon, to balance the sudden appearence of a photon and to conserve energy a virtual anti-photon* has to appear which must have equal but negative energy.


 

Pair Production is  a common phenomenon in electromagnetic radiation and has to do with the duality of matter existing as a particle and a wave. It produces one photon and antiphoton. I'm assuming that it is the antiphoton that enters the black hole. As with all matter/antimatter interaction, this causes 100% anihilation when coming into contact with the direct opposite of itself. All matter is converted to a pulse of electromagnetic radiation. This may be why the black hole loses mass. It would probably be measurable by bursts of electromagnetic radiation (X or Gamma I would surmise). Energy is conserved because the 100% energy/matter ineraction means nothing is lost.


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## Venusian Broon (May 9, 2013)

Foxbat said:


> Pair Production is a common phenomenon in electromagnetic radiation and has to do with the duality of matter existing as a particle and a wave. It produces one photon and antiphoton. I'm assuming that it is the antiphoton that enters the black hole. As with all matter/antimatter interaction, this causes 100% anihilation when coming into contact with the direct opposite of itself. All matter is converted to a pulse of electromagnetic radiation. This may be why the black hole loses mass. It would probably be measurable by bursts of electromagnetic radiation (X or Gamma I would surmise). Energy is conserved because the 100% energy/matter ineraction means nothing is lost.


 
Thoughts came to me this morning (sleeping on this did help!) 

Firstly I think the distinction between real and virtual particles is the key. The antimatter particle of the photon is the photon itself, so if it was some sort of process that pair-produced two real photons and the anti- got pulled into the black hole, it would add mass, as the antiphoton still has positive energy*. So the virtual photons produced are weirder. 

Think of it this way: there's a well known (real!) pair production event, when a gamma ray of the right energy can produce an electron and an anti-electron. These can combine and produce the same energy gamma ray again. This reaction obeys all postulated and observed conservation laws. 

Now look at virtual pair production in a vacuum - which is the source of our particles for the black hole. If an virtual electron pops into existence in the 'frothy foam' of quantum space, conservation laws, namely fermion conservation and charge conservation (?), dictate that a virtual positron must also appear - thus pair production. Then they interact and annhilate each other to produce...erm...well a real electron annhilating with a real positron must produce a gamma ray, but in the virtual case, the total energy of the system must be zero, thus no gamma ray can be produced (i.e. there wasn't one at the start, just a patch of vacuum). I'm going out on a limb,as I don't know if this is how they think of it, but this suggests to me that the *virtual positron must therefore have the additional property of having negative energy* to therefore conserve the total energy. The problem with negative energy particles is that, (again I think) we've never experienced one in real life as they probably shouldn't exist as stable particles in reality**. So this is why we talk of virtual particles instead of real - they are transitory states of QM interactions. 

This applies to our virtual photon outside the black hole, to conserve energy it must produce a negative energy anti-matter version of itself (i.e. not just the run of the mill real anti-matter version, because that just doubles the energy use and unbalances the poaching of 'free' energy even more...) 

I'm then guessing (actually so much out on a limb, I'm reaching my toes) that as stable negative energy photons are not allowed in our universe, the observer outside the black hole *can only see it emit real photons. *Thus the black hole must be a net gainer of negative energy photons, lose energy and by mass-energy equivalence, mass evaporates from it. 

(from memory*** wiki says a black hole the mass of the sun would produce blackbody radiation of temperature of ~0.2K - compare with the current 2.7K temperture of the afterglow of the big bang, so the photon are quite low energy infrared). 

Ursa - yes I think you're right in pointing out the importance of the surface area in these black hole discussions. The entropy of the black hole being somehow related to it's surface area is a dim and distant stirred memory from '_A Brief History of Time'_

Right I have to stop, my brain is overheating again. 


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* I'm pretty sure adding a photon of positive energy, via E = mc^2 (or the more complete complex version), makes the black hole heavier.
** they'd have really weird properties that would really make them stand out - like a magnetic monopole...
*** Yes I'm getting old, last night has become so long ago.


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## Foxbat (May 9, 2013)

@Venusian Broon
My brain is still wrestling with it but I think your explanation makes sense.


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## Venusian Broon (May 9, 2013)

I've come up with another way of (perhaps) explaining it. And it gets rid of all the negative energy stuff...


(Hopefully there are some theoretical astrophysicists out there that can comment on whether this analogy/explanation is valid. These are really just my rabid speculations - on so many levels ...)


Think of Hawking Radiation as a form of Quantum tunnelling. So a photon inside the black hole has a finite but very, very, very small probability of tunnelling through the event horizon, if we treat it as a barrier. Thus this process allows a photon to dissappear from inside the black hole and pop into existence back in the normal universe. (Hence no need for negative energy particles to fall in!) 

This causes the black hole to lose mass - because the energy/mass of the black hole is an extremely concentrated volume of extremely fundamental mass particles in equilibrium with a sea of photons (_maybe??? *)_. By removing some photons, this causes the system to compensate to 'cover those lost' by converting a little bit of mass into photons. 

This might also possibly help to explain why the Hawking radiation temperature goes up as the black hole gets lighter. Because the black hole is a finite volume and generally virtually impossible to escape from, it's geometry (_might??? **)_ confine the allowable wavelengths of EM radiation possible inside. Thus for a certain size of black hole there is a peak wavelength that is most likely to tunnel out. (Sun-mass black hole, is apparently the Infra-red photon which generates a black body temp of 0.27K, if I read it right.) 

When the mass starts to dissappear - the black hole itself gets smaller in actual size, and this starts to push this allowable wavelength smaller. Smaller wavelength being squeezed out means producing higher energy photons (hence higher BB temperature). Thus smaller black holes emit more energy and dissappear faster... 

...which is wot I believe Hawkings and his cronies came up with. 

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* I have no idea what should be inside the event horizon, but I do know that others have speculated - I'm assuming it's still 'ordinary' matter/energy but in some weird and very, very highly compressed state. 
** I'm using a guitar string analogy here - with a guitar string 50 cm long, fixed at both ends, you can't pluck a note that has a wavelength of 1 km. Similarly a black hole has very definite fixed boundaries.


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## Foxbat (May 10, 2013)

> Now look at virtual pair production in a vacuum - which is the source of our particles for the black hole. If an virtual electron pops into existence in the 'frothy foam' of quantum space, conservation laws, namely fermion conservation and charge conservation (?), dictate that a virtual positron must also appear - thus pair production. Then they interact and annhilate each other to produce...erm...well a real electron annhilating with a real positron must produce a gamma ray, but in the virtual case, the total energy of the system must be zero, thus no gamma ray can be produced (i.e. there wasn't one at the start, just a patch of vacuum). I'm going out on a limb,as I don't know if this is how they think of it, but this suggests to me that the *virtual positron must therefore have the additional property of having negative energy* to therefore conserve the total energy. The problem with negative energy particles is that, (again I think) we've never experienced one in real life as they probably shouldn't exist as stable particles in reality**. So this is why we talk of virtual particles instead of real - they are transitory states of QM interactions.


 
This is where I fail to grasp virtual particles.  If the total energy of the system is zero then - given the mass/energy relationship, there can be no mass. If this is the case, then how can something with zero energy/zero mass interact or affect anything that exists? however, I'm fully aware that it is probably me missing something important

Quantum tunneling sounds plausible though - especially given the sheer number of photons involved -  which would lower the probability of such events happening.


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## Moonbat (May 10, 2013)

What I don't get with the virtual particle pair explanation is that surely just as many pairs would pop into existence where the negative energy particle is outside the event horizon and the positive particle inside, so that the black hole would then gain some mass. Statistically these would balance out the ones that pop into existence the other way round resulting in a black hole that doesn't lose any energy or mass?

Hmm, but then the negative particle would soon be annihilated by a positive opposite particle in normal space (outside the black hole) which would create a burst of energy (gamma radiation?) which would look like it has come from the black hole, but that can't be right becuase then there is radiation 'leaking' from the black hole (although in this case it was created from just outside the event horizon) and the black hole would have gained some mass.


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## Venusian Broon (May 10, 2013)

Moonbat said:


> What I don't get with the virtual particle pair explanation is that surely just as many pairs would pop into existence where the negative energy particle is outside the event horizon and the positive particle inside, so that the black hole would then gain some mass. Statistically these would balance out the ones that pop into existence the other way round resulting in a black hole that doesn't lose any energy or mass?


 
My thinking floundered at first at this point i.e. wouldn't equal numbers of each be captured? but my guess was that negative energy _real_ particles are not allowed by the universe, so only positive energy real photons can possibly escape - therefore by the process that created the virtual pair, that means that a net influx of negative energy particles _must_ go into the black hole, as a net surplus of their positive energy partners escaped (The fact that a photon is it's own anti-particle and does not have a charge probably helps enormously, as perhaps it doesn't matter which of the two gets caught, the other one becomes a real photon).



> This is where I fail to grasp virtual particles. If the total energy of the system is zero then - given the mass/energy relationship, there can be no mass. If this is the case, then how can something with zero energy/zero mass interact or affect anything that exists? however, I'm fully aware that it is probably me missing something important


 
Yep, the way I'm picturing them - they are transitory 'things' that for the purposes of our calculations have some of the properties of other objects that we call real particles. So they can get away with all sorts of weird stuff. So they behave as if they have mass...but if the pair are left to their own devices and not converted into real particles, it's not actually real mass. Perhaps we should call it virtual mass 

Perhaps another way to think of it, is that we postulate that a vacuum has an energy state. Then we can allow this energy level to flucuate, so that for a fleeting moment, the extra energy can be borrowed to make some mass in the form of particles. But as this is 'borrowed' energy they must quickly dissappear.

Of course it need not only be a couple of particles are produced - the flucuation might be huge - large numbers of particles might pop into existence...which leads us logically to the concept of the Quantum Boltzmann Brains - a subject I find fascinating, but at the same time a little scary. And not the topic of this thread. 


p.s. after my last post, I did a bit of digging but as I didn't do General Relativity much at undergraduate or at all in my PhD, it was quite frankly full of technicalities I hadn't pondered and a world of hurt . Needless to say I'd guess most of that post was way wide of the mark! However I do believe the first bit - the analogy with Quantum tunnelling is acceptable.


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## Foxbat (May 10, 2013)

> Perhaps we should call it virtual mass


Perhaps with a virtual Higgs Boson?


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## Tor__Hershman (Jun 24, 2013)

Stephen Hawking is an amazingly brilliant being.
Of course my definition of *genius is*,
"Not only being much more intelligent than the vast majority of people, most of the time, but also...being more intelligent than yourself.....at times.

I use Einstein's Cosmological Constant as a prime example of yourself
& Bertrand Russel's desire to have, as I understand it, blown-up Stalin as most of the time.

Frankly, the words to The Third Rock From The Big Band Theory's theme should begin with the words, 
"*The whole universe wasn't then it was*" 'cause it 'twere not, accordin' to Tor, in a Big Dot.  

Prof. Hawking is a quintessentially, stupendously vast intellect BUT he do try to shuffle equations to fit areas, before our universe existed (Math is a function *of* our universe), where mathematics just ain't got any relevance.


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