Discussion in 'Physics & Math' started by The God, Mar 10, 2017.

1. ### The GodValued Senior Member

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This topic just popped in some other thread, we will see few crucial aspects of this, to understand the possibility of HR actually evaporating the Black Hole. For base reference wiki can be referred.

For HR.

1. The associated fluctuation is required to take place at just this side of Event Horizon.

A. What is so special about EH or just near EH that such fluctuation to take place? For a very massive BH, the EH is as tidal free as any other region of space, no big deal curved space time at EH.

B. Assuming that fluctuation does happen, then what is the probability of its occurring exactly on this side of EH?

C. I read that event horizon is a 2 D entity, so what does this side of EH signify?

D. This fluctuation must be random, no specific time interval can be assigned. Then what is the significance of calculating evaporation time, is it not a purely statistical exercise.

2. Which is a bigger effect? Absorption of CMBR by Black Hole or Hawking Radiation? If CMBR absorption is more then the beast would grow instead of evaporating?

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3. ### The GodValued Senior Member

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From wiki link on Hawking Radiation. This is pertinent for Sr#2 of OP.

"black hole of one solar mass (M) has a temperature of only 60 nanokelvins (60billionths of a kelvin); in fact, such a black hole would absorb far more cosmic microwave background radiation than it emits. A black hole of 4.5×1022 kg (about the mass of the Moon, or about 13 µm across) would be in equilibrium at 2.7 K, absorbing as much radiation as it emits. Yet smaller primordial black holes would emit more than they absorb and thereby lose mass."

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5. ### The GodValued Senior Member

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So when Hawking was talking about evaporation he was talking about premordial black holes only where CMB absorption was less than Hawking Radiation emission.

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7. ### RJBeeryNatural PhilosopherValued Senior Member

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As I understand it the required fluctuations occur all over the place, it's just near the hypothetical EH that the virtual particles can be physically separated.

8. ### The GodValued Senior Member

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That's nice, it suggest that gravity of BH near EH plays no role.

"Separated" here in a sense one goes inside EH so gone for eternity and another this side of EH effectively increasing the non BH type Mass of universe.

But there is a problem here in your proposition, the HR has a thermal characteristic which is dependent on BH Mass. So this fluctuation is BH specific.

9. ### RJBeeryNatural PhilosopherValued Senior Member

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I'm giving the "pop-sci" explanation, I don't claim to author it. In fact I have my own issues with this. Hell, even John Baez doesn't understand the popular explanation, check this out: http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html

Anyway the quantum fluctuations are not affected by the type of BH, but they are affected by the tidal forces at the EH; that's why a small BH is hotter than a large one. It's popular to say that a large enough BH has zero tidal forces at the EH but that will never be strictly true.

10. ### The GodValued Senior Member

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In stricter sense there is no relationship between tidal forces at BH and BH temperature. Your conclusion is although correct but non sequitur.

Thermodynamics around BH says that temperature is inversely proportional to mass. So a smaller BH will have higher temperature.

11. ### RJBeeryNatural PhilosopherValued Senior Member

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The tidal forces at the EH are inversely proportional to the mass of the BH...just as the temperature of the BH is inversely proportional to the mass of the BH. Therefore, the temperature of the BH is proportional to the tidal forces at the EH. It isn't a non sequitur, it's the layman's explanation of Hawking Radiation.

If you're looking for a criticism of this explanation then how about this: what mechanism makes the antiparticle more likely to fall beyond the EH while the particle escapes to freedom? If the virtual particles were equally likely to fall through the EH then there would be no net mass change in the BH over time.

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13. ### karenmanskerHSIRIBanned

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. . . . also MY understanding . . .

14. ### karenmanskerHSIRIBanned

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Spin, perhaps?

15. ### exchemistValued Senior Member

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That criticism had occurred to me too, but then I found I had misunderstood the process and in fact it is not claimed that the antiparticles are preferentially sucked in. From what I read (there was correspondence on physics stack exchange about it, here: http://astronomy.stackexchange.com/...king-radiation-why-only-capture-anti-particle), equal numbers of particles and antiparticles are radiated, but it is the energy of the BH that is lost in this process: due to energy/mass equivalence, the mass of the BH declines as its energy is exported via the mass and energy of the created particles and antiparticles.

To me, the key bit I do not understand so far is that the gravitation of the BH enables the virtual particles - which have a temporary existence in vacuum fluctuations and are in truth no more than disturbances in the field - to be somehow "boosted" into becoming real, permanent particles and antiparticles, i.e. pair production. I understand how very energetic interactions can result in pair production. But in this case it is a bit hard to envisage an "interaction" that only involves field disturbances in the vacuum and gravitation! I can only assume this is a nice piece of QED that is beyond me.

16. ### rpennerFully WiredRegistered Senior Member

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One way to think about "quantum fluctuations" is that they are a certain density of "noise" which propagates like all quantum fields do. So today's vacuum pair production is not an isolated blip but the deterministic cresting of the quantum fields which evolve from earlier field states. In such a model, the event horizon and space-time curvature induce different fates for those components of the noise that if it weren't for the horizon would skim the black hole.

Such a model allows testing of the analogue of Hawking radiation in an analog to a black hole, looking for thermal spectrums of phonons in a medium which is undergoing a transition from subsonic to supersonic flow.

http://www.nature.com/nphys/journal/v12/n10/abs/nphys3863.html

17. ### RJBeeryNatural PhilosopherValued Senior Member

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So if it takes energy for the pair production, and the particle/anti-particle don't immediately annihilate because they are separated due to the event horizon, then there is a net local loss of energy that apparently is balanced by being extracted from the black hole? That's a great way to explain it but it's still difficult to "internalize".

I don't have a problem with virtual particles becoming real particles. RPenner's explanation is good -- I subscribe to the idea of EM mass which means that, given the right circumstances, any particle can be created in a complex EM field.

18. ### exchemistValued Senior Member

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Yes it's still a bit of a conundrum.

One thing I had never thought about is the implication that, although you cannot extract information from inside the event horizon, you can apparently export energy!

19. ### The GodValued Senior Member

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Did not get you here..

Nothing is exported from inside the event horizon, not even energy.

20. ### RJBeeryNatural PhilosopherValued Senior Member

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If nothing, including energy, is extracted from inside the event horizon then the black hole would not evaporate. That is literally the theory of Hawking radiation.

21. ### The GodValued Senior Member

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That may be literally the theory of HR, but thats not the case. Nothing is extracted from inside the event horizon. May be you would like to read a bit more about HR (little bit more than pop science) to understand how black hole evaporates under HR theory without exporting anything from inside of EH.

22. ### exchemistValued Senior Member

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Don't be patronising! Cheap cracks about "pop science" are the sort thing I had hoped would stop with Paddo's departure from the forum. This has been a very polite discussion and interesting science, up to now. Please don't spoil it.

This is difficult stuff and none of us here, you included, are masters of it. So why don't we feel our way, together?

You say "nothing" is extracted from inside the event horizon, and yet Hawking Radiation proposes a mechanism by which energy is exported from the black hole, in the form of pair production outside the event horizon, such that the mass inside the event horizon decreases. The net effect is that mass is lost from inside the event horizon and is created outside it. Effectively, this is export of mass from the black hole, across the event horizon.

So it seems to me that your statement cannot be literally true, if Hawking radiation exists. At the very least, energy (and thus mass) is exported, surely?

Last edited: Mar 23, 2017
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23. ### RJBeeryNatural PhilosopherValued Senior Member

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I don't think literally means what you think it means. And all the nuance in the world cannot overcome logic -- if there is energy within the event horizon today, and that energy is not there tomorrow, then energy has indeed been extracted in some manner. In any event, I appreciate you suggesting wikipedia for a better understanding of Hawking radiation

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but I have no motivation to study it further; I've made my case in the other thread that HR itself requires a logical contradiction.