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The paradox of Hawking radiation - is matter infinitely compressible?


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The hypothetical Hawking radiation means that a set of baryons can be finally transformed, "evaporate" into a massless radiation - that baryons can be destroyed. It requires that this matter was initially compressed into a black hole.
If baryons can be destroyed in such extreme conditions, the natural question is: what is the minimal density/heat/pressure required for such baryon number violation? (or while hypothetical baryogensis - creating more baryons than anti-baryons).
While neutron star collapses into a black hole, event horizon grows continuously from a point in the center, like it this picture from: http://mathpages.com/rr/s7-02/7-02.htm
image003.gif
As radius of event horizon is proportional to mass inside, the initial density of matter had to be infinity. So if baryons can be destroyed, it should happen before starting the formation of event horizon - releasing huge amounts of energy (complete mc^2) - pushing the core of collapsing star outward - preventing the collapse. And finally these enormous amounts of energy would leave the star, what could result in currently not understood gamma-ray bursts.

So isn't it true that if Hawking radiation is possible, then baryons can be destroyed and so black holes shouldn't form?

We usually consider black holes just through abstract stress-energy tensor, not asking what microscopically happens there - behind these enormous densities ... so in neutron star nuclei join into one huge nucleus, in hypothetical quark star nucleons join into one huge nucleon ... so what happens there when it collapses further? quarks join into one huge quark? and what then while going further toward infinite density in the central singularity of black hole, where light cones are directed toward the center?

The mainly considered baryon number violation is the proton decay, which is required by many particle models.
They cannot find it experimentally - in huge room temperature pools of water, but hypothetical baryogenesis and Hawking radiation suggest that maybe we should rather search for it in more extreme conditions?
While charge/spin conservation can be seen that surrounding EM field (in any distance) guards these numbers through e.g. Gauss theorem, what mechanism guards baryon number conservation? If just a potential barrier, they should be destroyed in high enough temperature ...

Is matter infinitely compressible? What happens with matter while compression into a black hole?
Is baryon number ultimately conserved? If yes, why the Universe has more baryons than anti-baryons? If not, where to search for it, expect such violation?
If proton decay is possible, maybe we could induce it by some resonance, like lighting the proper gammas into the proper nuclei? (getting ultimate energy source: complete mass->energy conversion)
Is/should be proton decay considered in neutron star models? Would it allow them to collapse to a black hole? Could it explain the not understood gamma-ray bursts?

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The hypothetical Hawking radiation means that a set of baryons can be finally transformed, "evaporate" into a massless radiation - that baryons can be destroyed. It requires that this matter was initially compressed into a black hole.

 

 

Where are these baryons destroyed? What is the massless radiation?

 

The wikipedia article you cited:

A slightly more precise, but still much simplified, view of the process is that vacuum fluctuations cause a particle-antiparticle pair to appear close to the event horizon of a black hole. One of the pair falls into the black hole whilst the other escapes. In order to preserve total energy, the particle that fell into the black hole must have had a negative energy (with respect to an observer far away from the black hole).

 

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Swansont, I don't know where exactly these baryons are destroyed. The fact is that initially there were baryons, and finally they are no longer - like in proton decay or baryogenesis, the baryon number is not conserved.

About the "massless radiation", they usually expect some EM radiation (anyway, I don't know any massless baryons?)

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Swansont, I don't know where exactly these baryons are destroyed. The fact is that initially there were baryons, and finally they are no longer - like in proton decay or baryogenesis, the baryon number is not conserved.

About the "massless radiation", they usually expect some EM radiation (anyway, I don't know any massless baryons?)

So you are hypothesizing that it happens, and then claiming a paradox? The description of Hawking radiation does not have a mechanism that destroys baryons.

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Ok, it is not exactly a paradox, but just a self-contradiction: if baryons are not indestructible, they should be destroyed before reaching infinite density required to start forming the event horizon.

There's nothing in the theory that requires this. GR is independent of the standard model and is classical (i.e. not QM); it doesn't say what happens to the particles.

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I am not asking about some specific theory, but the reality.

Black hole evaporation requires that baryons are destructible, while formation of event horizon requires reaching infinite density in the center of neutron star - requires that matter can be infinitely compressed, without destruction of its baryons - contradiction.

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I am not asking about some specific theory, but the reality.

Black hole evaporation requires that baryons are destructible, while formation of event horizon requires reaching infinite density in the center of neutron star - requires that matter can be infinitely compressed, without destruction of its baryons - contradiction.

There is nothing in the theory that requires the destruction of baryons.

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Why assume baryon number is conserved at the ( possible ) singularity ?

After all we can consider time and space to be interchanged, with resultant causality violations.

Things which would make little sense to outside, distant observers are common inside black holes.

Further we know that matter/antimatter creation/destruction was not in equilibrium in the early universe at similar energy density.

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Swansont, Huge amount of baryons form a star, which collapses ... and then "evaporates" into massless radiation.

Lots of baryons in the beginning ... pooof ... none at the end - how it is not baryon destruction? Maybe they have just moved to an alternative dimension or something? smile.png

 

MigL, so is baryon number ultimately conserved? Could there be created more baryons than anti-baryons in baryogenesis? Can baryons "evaporate" through Hawking radiation?

Edited by Duda Jarek
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Swansont, Huge amount of baryons form a star, which collapses ... and then "evaporates" into massless radiation.

What theory predicts this?

 

Lots of baryons in the beginning ... pooof ... none at the end - how it is not baryon destruction? Maybe they have just moved to an alternative dimension or something? smile.png

What theory states that any part of star formation or collapse destroys baryons?

 

Find me a quote that says this. The text itself, not your misinterpretation of the text.

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I think you've chanced upon the Information Paradox. There are thoughts that if Hawking radiation does exist, then the informational content is preserved in some other fashion. Very open ended subject at the moment.

 

 

hmmm no it's not open in mainstream any more. Hawking retracted his statement concerning loss of information. Instead, the information is jumbled up inside the black hole, then leaves the black hole through information tunnelling.

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hmmm no it's not open in mainstream any more. Hawking retracted his statement concerning loss of information. Instead, the information is jumbled up inside the black hole, then leaves the black hole through information tunnelling.

 

 

I think you are being far too certain there. That information is not lost is conceded and hawking and kip thorne paid their dues - Susskind et al would argue through the holographic principle of string theory but others still argue why

 

Perhaps Hawking radiation is not the perfectly bland bb-like radiation it was speculated to be. Or it could well be that at the eh the principle of gr that would prohibit information from leaking from a bh breaks down, or flash of information at the moment of final evaporation, a remnant remains etc

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I'm mostly withholding judgement until we observe Hawking radiation. I don't doubt it does exist, I just don't like too much speculation on a speculation.

 

Anyways I think that is what OP is roughly describing. The possibility of Baryon number conservation violation. Considering we have real world observable violations, it is likely not the issue it has been made out to be.

 

I was thinking it might instead obey B-L conservation. Just a best fit approach though, not something I'd want to take to the bank.

Edited by Endy0816
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Anyways I think that is what OP is roughly describing. The possibility of Baryon number conservation violation. Considering we have real world observable violations, it is likely not the issue it has been made out to be.

 

 

We do?

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OK, I thought maybe I had missed some experimental result.

 

The bottom line here is that Baryon number is conserved in Hawking radiation. Duda Jarek's claims to the contrary are, as yet, unsupported.

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I must be being dense here.

 

Could we work on a seriously simplified model - an isolated and small black hole. A peanut falls into the black hole - aeons pass. The black hole becomes cooler than its surroundings and becomes a net radiator. Eventually the black hole evaporates entirely in a final flash of gamma radiation. All that has left the black hole is hawking (or similar) radiation. From the beginning of this paragraph to this point we have lost stuff. The protons and neutrons of the peanut (having 3 quarks each) had baryon number +1 the photons emitted (not being quark based) some of which will account for the mass-energy of the peanut have no baryon number. Surely that is a non-conservation of baryon number

 

http://books.google.co.uk/books?id=D6B59P8_OE8C&pg=PA89&lpg=PA89&dq=black+hole+baryon+number+conservation&source=bl&ots=uym2btBBQ4&sig=6i92feWQ9Upt6safBteljaPIdPQ&hl=en&sa=X&ei=2QFCUuiCD4aN7QaUwYHIBg&ved=0CFMQ6AEwBQ#v=onepage&q=black%20hole%20baryon%20number%20conservation&f=false

 

On this page (p89) Susskind says that qm of bh's must violate baryon number. Although he makes it clear that some baryons will be emitted in the final stages - it isnt all photons

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I'm mostly withholding judgement until we observe Hawking radiation. I don't doubt it does exist, I just don't like too much speculation on a speculation.

 

Anyways I think that is what OP is roughly describing. The possibility of Baryon number conservation violation. Considering we have real world observable violations, it is likely not the issue it has been made out to be.

 

I was thinking it might instead obey B-L conservation. Just a best fit approach though, not something I'd want to take to the bank.

 

We already know this kind of radiation will exist, it's analogue has presented itself in nature in the form of sonic black holes. So it's very very likely Hawking Radiation is permitted in nature as well.

 

http://books.google.co.uk/books?id=D6B59P8_OE8C&pg=PA89&lpg=PA89&dq=black+hole+baryon+number+conservation&source=bl&ots=uym2btBBQ4&sig=6i92feWQ9Upt6safBteljaPIdPQ&hl=en&sa=X&ei=2QFCUuiCD4aN7QaUwYHIBg&ved=0CFMQ6AEwBQ#v=onepage&q=black%20hole%20baryon%20number%20conservation&f=false

 

On this page (p89) Susskind says that qm of bh's must violate baryon number. Although he makes it clear that some baryons will be emitted in the final stages - it isnt all photons

 

Well that answers that question.

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I must be being dense here.

 

Could we work on a seriously simplified model - an isolated and small black hole. A peanut falls into the black hole - aeons pass. The black hole becomes cooler than its surroundings and becomes a net radiator. Eventually the black hole evaporates entirely in a final flash of gamma radiation. All that has left the black hole is hawking (or similar) radiation. From the beginning of this paragraph to this point we have lost stuff. The protons and neutrons of the peanut (having 3 quarks each) had baryon number +1 the photons emitted (not being quark based) some of which will account for the mass-energy of the peanut have no baryon number. Surely that is a non-conservation of baryon number

 

http://books.google.co.uk/books?id=D6B59P8_OE8C&pg=PA89&lpg=PA89&dq=black+hole+baryon+number+conservation&source=bl&ots=uym2btBBQ4&sig=6i92feWQ9Upt6safBteljaPIdPQ&hl=en&sa=X&ei=2QFCUuiCD4aN7QaUwYHIBg&ved=0CFMQ6AEwBQ#v=onepage&q=black%20hole%20baryon%20number%20conservation&f=false

 

On this page (p89) Susskind says that qm of bh's must violate baryon number. Although he makes it clear that some baryons will be emitted in the final stages - it isnt all photons

 

That's a good argument, and answers my question of what theory predicts this: quantum gravity will apparently have to include baryon number violation. But the violation is not in the Hawking radiation — making a particle and an antiparticle does not violate Baryon number — and it's not part of GR.

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Sure, Hawking radiation does not directly violate baryon number conservation, but only implies that destruction of baryons is possible.

 

If so, it should start happening before getting to infinite density in the center of neutron star, what is required to start forming the event horizon ...

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Before transforming into a black hole, it was a neutron star - I am asking about the starting moment of this transformation: when event horizon has just appeared in the center of the neutron star. Then it evolved to finally get out of its surface - from this moment we can call it a black hole.

 

As radius of event horizon is proportional to mass inside, mass is proportional to density times third power of radius, density of matter in the moment of starting event horizon in the center had to reach infinity first.

 

But if baryons are destructible, they should not survive this infinite compression - should be destroyed earlier, creating pressure inside and temporarily preventing the collapse ...

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Before transforming into a black hole, it was a neutron star - I am asking about the starting moment of this transformation: when event horizon has just appeared in the center of the neutron star. Then it evolved to finally get out of its surface - from this moment we can call it a black hole.

 

As radius of event horizon is proportional to mass inside, mass is proportional to density times third power of radius, density of matter in the moment of starting event horizon in the center had to reach infinity first.

 

But if baryons are destructible, they should not survive this infinite compression - should be destroyed earlier, creating pressure inside and temporarily preventing the collapse ...

 

If we consider a black hole as any object where the Schild radius is larger than the actual radius - then the eh will not expand out from a central point but rather from the position of the schild radius before the implosion.

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