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Does Hawking Radiation preclude EH formation?by rjbeery
Tags: black holes hawking 
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#1
Dec1112, 10:54 AM

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Discussions involving Hawking radiation in the study of black holes usually require their preexistence; however, if we apply the Hawking radiation process to the initial stages of a birthing black hole I'm confused about how the theory claims the event horizon would form in the first place.
In a simple nonrotating noncharged neutron star of, say, 4M the neutron degeneracy pressure would not be exceeded throughout the structure simultaneously; rather, it would occur at the center of the sphere where pressure is greatest. More specifically, it would occur between two neutrons at the center of the sphere, which would then allow further compacting of the surrounding matter, cascading into a traditional black hole. However, the Hawking black hole timetodissipate is given by: [tex]t_{\operatorname{ev}} = \frac{5120 \pi G^2 M_0^{3}}{\hbar c^4} \;[/tex] which is directly related to the mass of the BH as: [tex]8.410 \times 10^{17} \left[\frac{M_0}{\mathrm{kg}}\right]^3 \mathrm{s} \;[/tex] Our theoretical "minimalist" black hole would have a mass of two neutrons, or: [tex]M_0 = 2*1.6749*10^{27}{\mathrm{kg}} = 3.3498*10^{27}{\mathrm{kg}} [/tex] Which gives a timetodissipate as: [tex]8.410 \times 10^{17} \left[\frac{3.3498*10^{27}{\mathrm{kg}}}{\mathrm{kg}}\right]^3 \mathrm{s} \; = 3.1612 \times 10^{96} seconds[/tex] In other words, much, much shorter than Planck time! The original formation of the EH would theoretically dissipate more quickly than the cascading compaction could possibly propagate. The result would quickly become a similar structure of reduced mass...with no event horizon Has this concept been explored? 


#2
Dec1112, 11:05 AM

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PF Gold
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That is interesting. However, if you model formation of horizon from inside out, the horizon itself forms from the inside out. Hawking radiation is a horizon phenomenon. So the radiation from your instantly decaying initial black hole would be emitted in the center of the mass, almost immediately absorbed, and thus play no real role in avoiding mass/density criticality. That is, all mass energy stays put. Obviously, a real answer to what happens at the center of gravitational collapse awaits some solution to QM+GR.



#3
Dec1112, 11:12 AM

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PF Gold
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At least, that's how I see the standard "semiclassical" treatment of Hawking radiation working in this scenario. A fully quantum mechanical treatment might possibly give a different answer, but we don't have one yet. 


#4
Dec1112, 11:25 AM

P: 266

Does Hawking Radiation preclude EH formation?



#5
Dec1112, 11:36 AM

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PF Gold
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Also, as PAllen pointed out, for the emission of radiation to cause the BH to "evaporate", the radiation has to escape to infinity. (That's another assumption underlying the Hawking calculation, btw; the calculation doesn't work if the radiation doesn't escape to infinity.) Clearly that can't happen at the center of a neutron star. Even if such radiation were to form at the center of a neutron star when the horizon first forms, all it will do is increase the pressure at the center, but if the star starts out larger than the maximum mass, increasing the pressure at the center just makes it collapse faster (because the increased gravity due to the pressure pulls inward more than the increased pressure pushes outward). 


#6
Dec1112, 11:57 AM

P: 266

Regarding the reabsorption of the radiated energy, I considered that. However, the immediate local reabsorption is not guaranteed; in addition, the pressure must increase without a corresponding increase in temperature (as I understand it) in order to reach neutron degeneracy pressures, and temperature increases with such absorption. 


#7
Dec1112, 12:25 PM

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PF Gold
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One thing that won't shed any light on the matter is to cherry pick formulas to apply to a situation tens of orders of magnitude different from their range of applicability. 


#8
Dec1112, 01:14 PM

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#9
Dec1112, 01:23 PM

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PF Gold
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#10
Dec1112, 01:39 PM

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Thanks
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The question you have to be asking is whether the conditions are close enough to vacuum to trust a vacuum solution to provide accurate enough results, and it is clear that the center of a neutron star on the verge of gravitational collapse is <understatement>not that close to vacuum</understatement>. 


#11
Dec1112, 02:06 PM

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PF Gold
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#12
Dec1112, 02:34 PM

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#13
Dec1112, 02:44 PM

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PF Gold
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Hawking radiation is derived via semiclassical methods which are not expected to be valid near Planck energy. The Standard Model is expected to be wrong way before that. It is really common knowledge that no existing theory is expected to be valid in the center of a gravitational collapse. I don't have a convenient set of references handy. Perhaps someone else does. 


#14
Dec1112, 02:49 PM

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#15
Dec1112, 02:56 PM

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PF Gold
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"Under the assumption of an otherwise empty universe, so that no matter or cosmic microwave background radiation falls into the black hole, it is possible to calculate how long it would take for the black hole to dissipate:" The center of gravitational collapse is hard to accept as an approximation to 'an otherwise empty universe'. It is not 'nearly flat vacuum'. There is no thermal equilibrium. 


#16
Dec1112, 03:07 PM

P: 266

[tex]P = \frac{\hbar c^6}{15360 \pi G^2 M_0^2}\;[/tex] 


#17
Dec1112, 03:11 PM

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PF Gold
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Your "how exactly??" gets at the recurring issue: nobody knows; there is no established theory to apply here. 


#18
Dec1112, 03:13 PM

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PF Gold
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