Does Hawking Radiation preclude EH formation?

[concurrent discussion here]
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 non-rotating non-charged 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 time-to-dissipate is given by:

\(t_{\operatorname{ev}} = \frac{5120 \pi G^2 M_0^{3}}{\hbar c^4} \;\)

which is directly related to the mass of the BH as:

\(8.410 \times 10^{-17} \left[\frac{M_0}{\mathrm{kg}}\right]^3 \mathrm{s} \;\)

Our theoretical "minimalist" black hole would have a mass of two neutrons, or:

\(M_0 = 2*1.6749*10^{-27}{\mathrm{kg}} = 3.3498*10^{-27}{\mathrm{kg}} \)

Which gives a time-to-dissipate as:

\(8.410 \times 10^{-17} \left[\frac{3.3498*10^{-27}{\mathrm{kg}}}{\mathrm{kg}}\right]^3 \mathrm{s} \; = 3.1612 \times 10^{-96} seconds\)

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

Please Register or Log in to view the hidden image!

Has this concept been explored?

 

Log in or Sign up to hide all adverts.

I think the fact that your calculation shows a time that is less than Planck time is indicating the limitations of the equation not a physical reality. I aslo question you assumption of black holes forming from the compression of only 2 neutrons.

 

Log in or Sign up to hide all adverts.

Yes, lots of speculation here...

 

Log in or Sign up to hide all adverts.

there is nothing wrong with an answer being smaller than the plank time. we just will not be able to measure it. (not a comment on the post , just time)

 

RJ: What isn't speculation is that there are some massive objects out in space with huge gravitational fields that are physically very small. See this. And we can't see them, they aren't pouring out light, and in this respect black holes aren't hypothetical, even though you might legitimately challenge their exact nature. What is hypothetical however, is Hawking radiation. We have no actual evidence that it genuinely occurs. See this portion of the wikipedia article you linked to:

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). By this process, the black hole loses mass, and, to an outside observer, it would appear that the black hole has just emitted a particle.

Do you know of any actual negative-energy particles? Because I don't. And let's not forget that at an event horizon, which Hawking radiation does not challenge, gravitational time dilation is infinite as far as the distant observer is concerned. At that location the coordinate speed of light is zero according to the distant observer. So those vacuum fluctuations are occurring at a very slow rate indeed. Like a zero rate. You know, I think you should be asking instead about the "frozen star" concept. That was the original name for a black hole in Oppenheimer's time. Also have a read of the formation and growth of black holes by Kevin Brown:

"Incidentally, I should probably qualify my dismissal of the "frozen star" interpretation, because there's a sense in which it's valid, or at least defensible. Remember that historically the two most common conceptual models for general relativity have been the "geometric interpretation" (as originally conceived by Einstein) and the "field interpretation" (patterned after the quantum field theories of the other fundamental interactions). These two views are operationally equivalent outside event horizons, but they tend to lead to different conceptions of the limit of gravitational collapse. According to the field interpretation, a clock runs increasingly slowly as it approaches the event horizon (due to the strength of the field), and the natural "limit" of this process is that the clock just asymptotically approaches "full stop" (i.e., running at a rate of zero) as it approaches the horizon. It continues to exist for the rest of time, but it's "frozen" due to the strength of the gravitational field. Within this conceptual framework there's nothing more to be said about the clock's existence. This leads to the "frozen star" conception of gravitational collapse..."

I think you should also be asking about the gravastar too. This is described as an "alternative to the black hole theory" despite it being more like the original frozen star than current black hole theory. And since it features "a void in the fabric of space and time", it's even more of a hole than a black hole with a point singularity in the middle.

 

RJBeery

First, the Event Horizon is not a structure, it is the radius at which light no longer can escape. It is an optical illusion just like a rainbow is, it does not really have any existence but is a product of a certain level of gravitational energy. If you were falling toward a sufficiently large BH you would not know when you crossed the EH.

Second, Hawking Radiation is a result of quantum activity OUTSIDE of the EH, The EH CAUSES Hawking radiation by separating virtual particle pairs, swallowing one while the other escapes. The escaping particles ARE HR.

So your initial question is moot, it is not based on the actual situation, and there is HR simply because there is an event horizon, any EH of any size. Larger ones have less surface area/mass ratios so large BHs evaporate at much slower rates than small BHs.

Grumpy

Please Register or Log in to view the hidden image!

 

In part because you misunderstand both Hawking radiation and formation of an event horizon during gravitational collapse. Hawking radiation is a description of the vacuum of quantum field theory in a background curved space-time in the presence of an event horizon. It is, I believe, the first physical prediction of a phenomenon that is at the same time fundamentally gravitational, quantum and relativistic. It is not a prediction of any new theory of quantum gravity, but it should be the limiting form of any successful theory of quantum gravity in the limit of black hole mass being large compared to the fundamental scale of quantum gravity due to the need of such a theory to agree with GR and quantum field theory in the appropriate limits.
In GR, which is not a quantum theory, the event horizon in a gravitationally collapsing fluid grows very fast. Nothing prevents it from growing faster than the speed of light. Under such conditions, naive application of the Hawking radiation formula doesn't take into the account that the center of a neutron star is not a vacuum and the event horizon is not a static, material thing.
http://astroreview.com/upload/3419/Black_Hole_Horizons_and_How_They_Begin.pdf
Dieter Brill, "Black Hole Horizons and How They Begin" Astronomical Review (Jan 19, 2012).

Any legitimate (which is to say, reasonable and scientific) challenge would involve observations not currently in evidence and either proof of theorems of General Relativity or robust numerical simulation, not published anywhere. So in the putative sense that the best scientific theories have, both Hawking radiation and the actuality of black holes hold the highest level of truth status possible for scientific claims. They are theorems of the best tested physical theories of the day and violate no physical or logical assumptions.

A shocking confession of ignorance of Newtonian mechanics. Every satellite in the sky and bird in the air is at negative energy according to Newton's Universal Gravitation. In the physics of quantum field theory in curved space-time there are some more relevant examples, but the big picture is here Farsight has taken positivity of energy to be a law of nature when it is a consequence of some, but not all, physical theories and assumptions.

Too many oversimplifications and pop-physics concepts have left Farsight with a flawed understanding and a highly inflated opinion of his own competence.

That would be in 1939, over two decades since the publication of the Schwarzschild vacuum solution. But the essential property was published in 1916 by Johannes Droste.

The view is antique and chauvinistic as it respects only the clocks of the external observer. It is very natural for the physics of the external observe to say it takes an infinite amount of time to cross a one-way surface since physics otherwises allows motion between arbitrary locations. This surface that cuts one spatial part of the universe off from the rest naturally can only be approached in the limit of infinite time for the external physics. To the physics of someone crossing the event horizon, no such weirdness need apply, and the normal constraint of one's future remaining inside one's own lightcone is all that need apply.

It's also an extremely fringe idea with conceptual gaps not covered by calculation of how neutron stars suddenly develop an entirely hollow center. The citation counts of gravastar papers appear to all be < 60 with most < 10.

http://arxiv.org/abs/1008.0554

 

And that satellite or that bird has a positive mass which equates to positive energy. There are no negative-energy birds, and there are no negative-energy particles either. Do not confuse the convention whereby the reference location for zero gravitational potential is at infinite distance with the actual mass-energy of a body. A body at rest on the ground comprises less mass-energy than the same body in free space, but in both cases that mass-energy is positive.

 

Yes, the OP presumes a symmetrically spherical collapse. Your reference merely points out that this is atypical, not unphysical. In the real world we would expect the EH to form at various places within the neutron star's structure due to variations in pressures, densities, etc. Occurring simultaneously along some time slice is fine. Also, the EH itself (being a "property" rather than a physical entity) propagating at speeds faster than c is permissible due to this possibility, so the point you and Grumpy are trying to make doesn't apply; the EH growing due to the altered gravitational field of the existing EH must be constrained to c, unless you'd like to argue that gravity has no such limitation. Therefore, each individual, simultaneous "pocket" of EH formation occurring within the neutron star would be subject to the same analysis.

 

Except the Event Horizon is not a local feature that has altered local acceleration due to gravity. It is a global feature of space time with no local gravitation changes. For a spherical shell collapsing the Event horizon forms and grows from the empty center and expands at the speed of light to swallow the shell at precisely the moment it would be smaller than the shell's Schwarzschild radius. So your "analysis" betrays some points of misunderstanding.

You are taking an "actual mass-energy" from classical special relativity applying it to the quantum physics near a black hole where the correct frame independent quantity is something like "energy at infinity." My point remains that your calculation-free, pop-physics-based reasoning is based on only a pedestrian understanding of energy which is nothing more or less than than a particular conserved number from Noether's theorem from a continuous symmetry of a physical theory. Change the physical theory and you change the definition of energy. Energy is so much a derived quantity that Newton's Principia makes no mention of a conserved kinetic energy proportional to the square of velocity. (That would wait for Émilie du Châtelet and Gaspard-Gustave Coriolis of the eighteenth and nineteeth centuries, respectively. The special relativistic formulas, \(E \vec{v} = c^2 \vec{p}\) and \(E^2 - \left( c \vec{p} \right)^2 = \left( m c^2 \right) ^2\), would have to wait to the twentieth century.)

 

Yes, my misunderstanding has been betrayed.

Please Register or Log in to view the hidden image!

One thing is clear, which is that nobody really knows the details of how these are formed so my questions and naive speculations are hardly countered by your apparent definitive assessments.

 

Maybe this concept has been explored, I have heard in internet forums that some people think that microscopic black holes would just evaporate if they where created at the LHC. I don't have a link to that since the myspace forums was deleted. But, I don't think the ratio between the size of the event horizon and the occurance that this event horizon would come into contact with particle pairs being created in space is described in these equations. A particle pair may only accure appoximately once every cubic or so meters. The event horzin in question would be much smaller than that, and then have a far less likely chance to come into contact with the event horizon. A microscopic black hole would have a far greater chance to come into connact with air in a vacuum before it would come into connact with a random particle pair being created near the microscopic black hole. In other words, it would gobble up everything near it before Hawking Radiation even had a chance to affect it. The event horizon could come into connact with something else before it comes into a cotact with a particle pair being created nearby it. I don't think these equations alone really describe everything that would be going on in that hypothetical situation. It would be much different in normal situations where the black hole is formed from a massive star in a large vacuum of space, not artificial recreations in a lab. So then that would only be an approximation of what happens since it does not consider the size of the EH and the likely hood that it comes into contact with a particle pair. If this happend in space around a star it would be far more likely and the consideration wouldn't be necassary. It would be large enough to encounter many particle pairs.

 

Hi RJ,

Here's a non-rigorous way of thinking about this which may or may not be of use.

Consider pressure. A neutron star collapses into a black hole when neutron degeneracy pressure is no longer able to resist the pressure to to gravity.

Given that there is no limit to the inward pressure due to gravity, then for a black hole to never form, there must be some similarly limitless counteracting pressure.

So, could Hawking radiation provide unlimited pressure? I suspect not, since the radiation is most intense (implying maximum pressure?) when the hole is smallest.

 

Hi Pete, I have a problem with the bolded part. I see it as a limitation of GR, not a description of reality. Anyway ATYY posted the these links at Physics Forums in a thread on the same subject which I found interesting.

 

I don't understand what you mean.
Is there any theory that suggests a limit to pressure applied by gravity? How would that work?

 

As long as one approaches gravity as a force within the context of GR, probably not... However this also leads to the concept of the point singularity, which introduces difficulties of its own, where efforts to unify GR and QM are concerned.

If gravity is approached as an emergent function of QM, an unlimited force of gravity is less likely, and the "point singularity" likely an artifact of mathematics. As successful as GR has been we are begginning to see limitations in its unqualified application at both quantum and cosmological scales.

The conflict between the QM and locally defined scales of the space-time of GR have been around for as long as the two have coexisted. It has really only been the last few decades that GR, as traditionally understood, has been reaching it limits of unquestioned applicability, at cosmological scales.., as the introduction of first dark matter and then dark energy have been required to extend GRs usefulness, at the involved scales that each of these unknown variables (dark matter and energy) have become necessisary.

So, from a purely theoretical point of view of GR, there may be no limit to the potential force of gravity. But GR does not provide much insight into the fundamental origins of gravity. And though there has yet been no real success in the search for a consistent model of quantum gravity, it does appear it is from the context of QM that progress, will be discovered. Though even this may require a conceptual evolution in how we ultimately come to understand both GR and QM.

I am not sure your question, "How would that work?", can be answered at this time. At the same time I can see no way that an unlimited gravitational force or preassure resulting from gravitational force, can be consistent with a fundamental QM origin.

 

rpenner said:

"Except the Event Horizon is not a local feature that has altered local acceleration due to gravity. It is a global feature of space time with no local gravitation changes. For a spherical shell collapsing the Event horizon forms and grows from the empty center and expands at the speed of light to swallow the shell at precisely the moment it would be smaller than the shell's Schwarzschild radius. So your "analysis" betrays some points of misunderstanding."

Exactly. Have a great holiday rpenner.

 

One thing that is not mentioned is, gravity not only contracts space-time, but it also causes phase changes that can differ, reference to reference, in the space-time well. The solid iron core of the earth has solid iron existing at a temperature much higher than its normal melting point. On the surface iron would be a gas. Same material, but different phases in the well.

This is because the gravity induced pressure physically alters the orbital distances allowing a new material phase for the iron. This occurs apart from space-time changing, since you can create the same phases even without gravity such as with hydraulic presses. You can make solid iron at the space-time reference of the surface using the press. The press does not alter space-time, except in a tiny density connected way. You can make the same iron phase in Jupiter if we depressurize. Space-time will stay contracted.

It follows that the formation of a black hole will more than likely result in additional phase changes, because of hydraulic pressures, beyond the neutrons of neutron density. This might also explain why energy does not appear to escape; the new phases don't give off the expected energy.

If you assume earth's core iron has to behave like iron on the surface, you would expected highly ionized iron but won't see it. You would need to use a better assumption connected to solid state output not vapor output.

 

Uhh, are you asking for my personal treatise on quantum gravity? Hmm. Anyway, I have a problem with accepting physical infinities of any sort and I am not the only one that feels this way.

 

We're not talking of infinities, so I still don't understand what you mean.
And I'm not sure how quantum gravity is relevant, because the pressure in question (the inward pressure of gravity) works at a classical macroscopic level.