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Questions about black holes and the Hawking radiation.


lucks_021

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12 minutes ago, lucks_021 said:

Do we have any evidence that black holes actually emit radiation? If not, how can we prove it? If so, is Hawking radiation the best way we have to explain it?

 

Hawking Radiation has as yet, never been detected, but it is a reasonable scientific argument based on the quantum nature of EH's and virtual particle pairs. 

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2 hours ago, lucks_021 said:

Do we have any evidence that black holes actually emit radiation? If not, how can we prove it? If so, is Hawking radiation the best way we have to explain it?

Any Hawking radiation emitted by black holes would be too little to be detected. Only really tiny black holes would emit detectable amounts of radiation.

So, no, there is no evidence that black holes emit radiation.

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On 4/14/2019 at 4:16 AM, Strange said:

Any Hawking radiation emitted by black holes would be too little to be detected. Only really tiny black holes would emit detectable amounts of radiation.

So, no, there is no evidence that black holes emit radiation.

I have a question that is puzzling me.  I assume my problem is due to only seeing the 'pop science' explanation of Hawking radiation, anyway....

If there is pair production near the event horizon and 1 particle falls into the BH and the other escapes, how would that decrease the mass of the BH?  Didn't a particle enter the BH and increase it's mass?

Edited by Bufofrog
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24 minutes ago, Bufofrog said:

I have a question that is puzzling me.  I assume my problem is due to only seeing the 'pop science' explanation of Hawking radiation, anyway....

If there is pair production near the event horizon and 1 particle falls into the BH and the other escapes, how would that decrease the mass of the BH?  Didn't a particle enter the BH and increase it's mass?

So the "pair production" is a very simplified analogy. I have seen a better description terms of positive and negative energy (which, I believe, more accurately represents what the math says) but I haven't been able to find it again.

But if we stick with the virtual pair explanation, one way of thinking about this is the energy bookkeeping required. For the two particles to be separated, they have to be given energy equivalent to the mass of the two particles in order to convert them to "real" particles. One of the particles falls into the black hole, returning that mass-energy to the black hole. The other ne escapes taking that mass-energy with it.

That just moves the question to: "where does the energy come from to make the particles real?" From the black hole's gravitational field. As far as I know, the only way of understanding the details of that is to get into the (very complex) math involved.

Another way of thinking about it: the virtual particle pair have net zero energy, so you can think of one having positive energy and one having negative energy. As particles with negative energy don't exist, the one that escapes must have positive energy and the one that falls in subtracts energy (mass) from the BH.

There are also explanations in terms of particles escaping the event horizon by quantum tunnelling. 

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5 minutes ago, Strange said:

Another way of thinking about it: the virtual particle pair have net zero energy, so you can think of one having positive energy and one having negative energy. As particles with negative energy don't exist, the one that escapes must have positive energy and the one that falls in subtracts energy (mass) from the BH.

That actually makes some sense to me.  The difficulty is that I can't help but try to visualize this stuff as it relates to my everyday experience which does not work.    

Thanks for the insight and help Strange, I have to go take a couple of aspirins now... :) 

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55 minutes ago, Bufofrog said:

I have a question that is puzzling me.  I assume my problem is due to only seeing the 'pop science' explanation of Hawking radiation, anyway....

If there is pair production near the event horizon and 1 particle falls into the BH and the other escapes, how would that decrease the mass of the BH?  Didn't a particle enter the BH and increase it's mass?

Good question, and one many ask. For a typical stellar mass range BH, the 'particle-antiparticle pairs' will not be say electron-positron, but overwhelmingly just very low frequency photons. Now it's a fact that a photon is it's own antiparticle. Which sort of makes it very hard how to see one can be assigned positive energy, while the other, nominally identical member somehow carries negative energy!
Best I can tell, and I'm definitely no expert here, this is gotten around by imo a very dubious 'trick'. We start with the standard Planck definition E = hv, where v is the frequency of a given photon in some static frame just outside the EH. By assigning a local coordinate system, we then define 'positive frequencies' to propagation in say the radial outward direction, and 'negative frequencies' to inward radial propagation. Which is formally ok for use in a say a waveguide setting any EE would be familiar with. But no such EE would take seriously the notion that waves propagating along say -z axis really possess 'negative energy' whereas only the +z propagating waves carry positive energy.

Anyway, seems to me HR buffs actually make the formal assignment E = hv = negative for the locally assigned negative propagation sense i.e. inward radial motion. It's evidently additionally justified by formally equating negative frequency' with a 'positive frequency' particle i.e. photon, 'traveling backwards in time'. Somehow that strengthen the argument for 'negative energy', but I'm not clear how!

Apart from the matter of whether an EH, which is necessary for this picture to give HR, exists, I find the above line(s) of reasoning, drastically oversimplifying perhaps, to be very suspect indeed.

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Here is an attempt to explain what the math actually describes: http://www.desy.de/user/projects/Physics/Relativity/BlackHoles/hawking.html

It seems to build down to the fact that different frames of reference will calculate the energy of the quantum vacuum differently. So if you compare the energy seen by a notional observer an infinite distance away with another observer before the black hole formed, you can calculate a difference that corresponds to Hawking radiation.

Another (more readable) overview here: http://backreaction.blogspot.com/2015/12/hawking-radiation-is-not-produced-at.html

She also draws the analogy with Unruh radiation: the fact that an accelerating observer should see energetic particles arising from the quantum vacuum. (Note that someone free-falling into a black hole would not see any Hawking radiation)

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6 hours ago, Bufofrog said:

That actually makes some sense to me.  The difficulty is that I can't help but try to visualize this stuff as it relates to my everyday experience which does not work.    

Thanks for the insight and help Strange, I have to go take a couple of aspirins now... :) 

Virtual particle pair production is a fact. Therefor I don't see nothing too extraordinary in contemplating this same virtual particle production just this side of a BH's EH. Which leaves us a couple of options...both annihilate and that's that...one escapes thereby becoming real and positive, and one falls in becoming negative to maintain conservation laws, and so subtracting mass from the BH.

So while it is difficult and near impossible to detect, it seems to me at least to be a reasonable assumption. That view is discussed here.....

https://phys.org/news/2014-09-black-hole-thermodynamics.html

 

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Even if you consider just low energy virtual photons, you still need to satisfy conservation laws.
You cannot simply have one heading towards the EH. Conservation of momentum dictates its opposing virtual photon is headed away from the EH.
And once one of the virtual pair is removed by the BH's EH, the other of the pair becomes a real low energy photon or Hawking Radiation.
But those pesky conservation laws again dictate that the energy debt must be repaid, as virtual particles live on borrowed time, and so, the BH gives up that amount of mass/energy to make the re-payment.

I don't see the problem Q-reeus, maybe you can elaborate. 

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10 minutes ago, MigL said:

Even if you consider just low energy virtual photons, you still need to satisfy conservation laws.
You cannot simply have one heading towards the EH. Conservation of momentum dictates its opposing virtual photon is headed away from the EH.
And once one of the virtual pair is removed by the BH's EH, the other of the pair becomes a real low energy photon or Hawking Radiation.
But those pesky conservation laws again dictate that the energy debt must be repaid, as virtual particles live on borrowed time, and so, the BH gives up that amount of mass/energy to make the re-payment.

I don't see the problem Q-reeus, maybe you can elaborate. 

Merely stating that the usual conservation laws must be respected is not enough. Detail matters. As I said I'm no expert but find the usual picture unsatisfying.
Let me throw this back to you. What exactly is the 'negative energy' entity that enters inside the BH EH? Recalling my uncontroversial point photons are their own antiparticles.

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7 minutes ago, Q-reeus said:

Merely stating that the usual conservation laws must be respected is not enough. Detail matters. As I said I'm no expert but find the usual picture unsatisfying.
Let me throw this back to you. What exactly is the 'negative energy' entity that enters inside the BH EH? Recalling my uncontroversial point photons are their own antiparticles.

The detail requires things like the Bogoliubov transformation to define quantum theory on a curved spacetime 

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5 minutes ago, MigL said:

I did not call it negative energy. There is no such thing,
But virtual particles must re-pay their borrowed energy according to Heisenberg.
So the 'accountant' puts it in the - column.

What?! It's clear in HR picture that what escapes to 'infinity' is positive energy real photons. To balance the energy ledger, you *must* have something possessing 'negative energy' entering inside the BH EH. Again - what can those somethings be?

3 minutes ago, Strange said:

The detail requires things like the Bogoliubov transformation to define quantum theory on a curved spacetime 

See my reply to MigL

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The following article and paper supporting Hawking Radiation stimulating from an Analogue BH certainly adds support along with the other reasons such as the law of conservation, as to why Hawking Radiation is generally accepted by most physicists today as a very reasonable assumption......

https://physicsworld.com/a/physicists-stimulate-hawking-radiation-from-optical-analogue-of-a-black-hole/

extract:

"Few doubt that this Hawking radiation, predicted in 1974, is a real phenomenon – but no-one has ever seen it. Direct astronomical observations are very challenging because the radiation is too feeble; the X-rays streaming from suspected black holes are instead emitted by incredibly hot gas as it spirals inwards. But researchers believe that the equivalent of Hawking radiation might be seen emerging from laboratory experiments that mimic black holes in other media, such as light, acoustic or water waves. Now, a team at the Weizmann Institute of Science in Rehovot, Israel, has reported experiments that they say come one step closer to producing Hawking radiation in an “optical black hole”.

Virtual particles drive Hawking radiation:

"Hawking radiation is caused by quantum events near the event horizon. According to quantum theory, the vacuum of empty space is alive with “virtual particles”: pairs comprised of a subatomic particle and its antiparticle (such as an electron and positron), which may pop briefly into existence in a random quantum fluctuation before annihilating one another. But at the event horizon, one of the pair might fall into the back hole while the other escapes and becomes a real particle. This process draws gravitational energy from the black hole, in effect lowering its mass. In this way the black hole slowly evaporates as Hawking radiation streams from its surface".

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.010404

Observation of Stimulated Hawking Radiation in an Optical Analogue:

ABSTRACT:

The theory of Hawking radiation can be tested in laboratory analogues of black holes. We use light pulses in nonlinear fiber optics to establish artificial event horizons. Each pulse generates a moving perturbation of the refractive index via the Kerr effect. Probe light perceives this as an event horizon when its group velocity, slowed down by the perturbation, matches the speed of the pulse. We have observed in our experiment that the probe stimulates Hawking radiation, which occurs in a regime of extreme nonlinear fiber optics where positive and negative frequencies mix.

"The fact that both the mathematics is so similar and that observations in the analogues are what is predicted gives, to me at least, additional weight to Hawking’s predictions."

William Unruh, University of British Columbia

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

https://arxiv.org/abs/1809.00913

Observation of thermal Hawking radiation at the Hawking temperature in an analogue black hole:

Submitted on 4 Sep 2018 

"We measure the correlation spectrum of the Hawking radiation emitted by an analogue black hole and find it to be thermal at the Hawking temperature implied by the analogue surface gravity. The Hawking radiation is in the regime of linear dispersion, in analogy with a real black hole. Furthermore, the radiation inside of the black hole is seen to be composed of negative-energy partners only. This work confirms the prediction of Hawking's theory regarding the value of the Hawking temperature, as well as the thermality of the spectrum. The thermality of Hawking radiation is the root of the information paradox. The correlations between the Hawking and partner particles imply that the analogue black hole has no analogue firewall."

36 minutes ago, MigL said:

I did not call it negative energy. There is no such thing,
But virtual particles must re-pay their borrowed energy according to Heisenberg.
So the 'accountant' puts it in the - column.

Hi MigL...Just a thought...doesn't this just apply to "real particles" ? It shouldn't apply to virtual particles I suggest. 

 

Edited by beecee
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12 hours ago, Q-reeus said:

Good question, and one many ask. For a typical stellar mass range BH, the 'particle-antiparticle pairs' will not be say electron-positron, but overwhelmingly just very low frequency photons. Now it's a fact that a photon is it's own antiparticle. Which sort of makes it very hard how to see one can be assigned positive energy, while the other, nominally identical member somehow carries negative energy!

That’s not how it’s done.

the pair has an energy deficit which is fine as long as they recombine before the HUP is violated. The BH must provide that energy if the BH swallows up one of the particles.

 

2 hours ago, beecee said:

Hi MigL...Just a thought...doesn't this just apply to "real particles" ? It shouldn't apply to virtual particles I suggest. 

Once the BH consumes one, they become real.

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6 minutes ago, swansont said:

That’s not how it’s done.

the pair has an energy deficit which is fine as long as they recombine before the HUP is violated. The BH must provide that energy if the BH swallows up one of the particles.

 

You also fail to answer my question. What exactly are the 'particles' or more specifically 'quanta' that get swallowed up? Vague hand-waving about 'the BH gives up some energy' just doesn't near cut it.

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23 minutes ago, swansont said:

Once the BH consumes one, they become real.

Of course, thanks. What do you think of the two papers showing Hawking Radiation as valid via optical analogue? And do you agree with my assessment, that Hawking Radiation appears a logical concept?

19 minutes ago, Q-reeus said:

You also fail to answer my question. What exactly are the 'particles' or more specifically 'quanta' that get swallowed up? Vague hand-waving about 'the BH gives up some energy' just doesn't near cut it.

I don't believe that any scenario upholding the law of conservation is hand waving...Pretty solid indirect evidence in my book. Ignoring it [law of conservation] is ridiculous.  

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Does it matter if they are particles, or quanta, as you seem to think there is a difference ???

These virtual pairs exist on energy borrowed from the universe, for a brief period of time according to Heisenberg's Uncertainty Principle.
And once that time is up the debt must be re-paid to the universe according to stdev(E)*stdev(t) >= hbar/2.

If one of the virtual particles ( or quanta ) is no longer available to annihilate with the other, it must become a real ( Hawking ) particle or quanta.
That means the universe is owed the equivalent of TWO particle's mass/energy by the Black Hole which has caused this debt.
The Black Hole, however, has swallowed ONE particle's mass/energy, so the net effect is that it loses the equivalent of ONE particle's mass/energy.

Where is this negative you speak of ???
If I owe you money, does it mean I give you negative currency ???

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3 hours ago, beecee said:

...I don't believe that any scenario upholding the law of conservation is hand waving...Pretty solid indirect evidence in my book. Ignoring it [law of conservation] is ridiculous.  

More ridiculous still is to attribute to me something I have never implied. Get your facts straight!

1 hour ago, MigL said:

Does it matter if they are particles, or quanta, as you seem to think there is a difference ???

Of course not. It's just that 'particles' typically conjures up the image of electron/positron pairs, whereas as I mentioned earlier in reality it's typically very low frequency/long wavelength photons that are notionally involved. Hence 'quanta' conveys that somewhat better.

1 hour ago, MigL said:

These virtual pairs exist on energy borrowed from the universe, for a brief period of time according to Heisenberg's Uncertainty Principle.
And once that time is up the debt must be re-paid to the universe according to stdev(E)*stdev(t) >= hbar/2.

If one of the virtual particles ( or quanta ) is no longer available to annihilate with the other, it must become a real ( Hawking ) particle or quanta.
That means the universe is owed the equivalent of TWO particle's mass/energy by the Black Hole which has caused this debt.
The Black Hole, however, has swallowed ONE particle's mass/energy, so the net effect is that it loses the equivalent of ONE particle's mass/energy.

That picture is quite non-standard. In the standard picture, the hole mass decreases owing to negative energy quanta being swallowed. Link to a reputable article where the accounting picture has positive energy quanta being swallowed. I do agree with this much of your own version - logically there must be a pair of positive energy photons created owing to tidal g ripping apart of a virtual pair. But to then say the BH field just adjusts down it's mass to compensate is precisely the kind of vague hand-waving I pulled Swansont up on earlier. HOW could that 'BH mass downward adjusting' happen?

1 hour ago, MigL said:

Where is this negative you speak of ???
If I owe you money, does it mean I give you negative currency ???

See above - any analogy to financial ledgers is woefully inadequate.

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1 hour ago, Q-reeus said:

More ridiculous still is to attribute to me something I have never implied. Get your facts straight!

8 hours ago, Q-reeus said:

Merely stating that the usual conservation laws must be respected is not enough. Detail matters. 

 

That sounds like ignoring them. Who doesn't respect the conservation laws? Certainly not Hawking or Hawking Radiation that its based on! In other words its more then enough!

Again the standard picture re Hawking Radiation, without direct observation, is thought to be a reasonable assertion. Two papers I have linked to even go as far as to say they have observed them in an analogous situations. 

More support for the reasonably obvious.....

The following by Steve Carlip; 

BA -- Harvard College, Cambridge, MA, 1975

Ph.D. -- University of Texas at Austin, 1987 (adviser: Bryce DeWitt)

Postdoc -- Institute for Advanced Study, Princeton, 1987-90

Faculty member, University of California at Davis, 1990-present

Interests: quantum gravity; classical general relativity; theoretical particle physics; mathematical physics

 

Hawking radiation

"There are a number of ways of describing the mechanism responsible for Hawking radiation. Here's one:

The vacuum in quantum field theory is not really empty; it's filled with "virtual pairs" of particles and antiparticles that pop in and out of existence, with lifetimes determined by the Heisenberg uncertainty principle. When such pairs forms near the event horizon of a black hole, though, they are pulled apart by the tidal forces of gravity. Sometimes one member of a pair crosses the horizon, and can no longer recombine with its partner. The partner can then escape to infinity, and since it carries off positive energy, the energy (and thus the mass) of the black hole must decrease.

There is something a bit mysterious about this explanation: it requires that the particle that falls into the black hole have negative energy. Here's one way to understand what's going on. (This argument is based roughly on section 11.4 of Schutz's book, A first course in general relativity.)

To start, since we're talking about quantum field theory, let's understand what "energy" means in this context. The basic answer is that energy is determined by Planck's relation, E=hf, where f is frequency. Of course, a classical configuration of a field typically does not have a single frequency, but it can be Fourier decomposed into modes with fixed frequencies. In quantum field theory, modes with positive frequencies correspond to particles, and those with negative frequencies correspond to antiparticles.

Now, here's the key observation: frequency depends on time, and in particular on the choice of a time coordinate. We know this from special relativity, of course -- two observers in relative motion will see different frequencies for the same source. In special relativity, though, while Lorentz transformations can change the magnitude of frequency, they can't change the sign, so observers moving relative to each other with constant velocities will at least agree on the difference between particles and antiparticles.

For accelerated motion this is no longer true, even in a flat spacetime. A state that looks like a vacuum to an unaccelerated observer will be seen by an accelerated observer as a thermal bath of particle-antiparticle pairs. This predicted effect, the Unruh effect, is unfortunately too small to see with presently achievable accelerations, though some physicists, most notably Schwinger, have speculated that it might have something to do with thermoluminescence. (Most physicists are unconvinced.)

The next ingredient in the mix is the observation that, as it is sometimes put, "space and time change roles inside a black hole horizon." That is, the timelike direction inside the horizon is the radial direction; motion "forward in time" is motion "radially inward" toward the singularity, and has nothing to do with what happens relative to the Schwarzschild time coordinate t.

The final ingredient is a description of vacuum fluctuations. One useful way to look at these is to say that when a virtual particle- antiparticle pair is created in the vacuum, the total energy remains zero, but one of the particles has positive energy while the other has negative energy. (For clarity: either the particle or the antiparticle can have negative energy; there's no preference for one over the other.) Now, negative-energy particles are classically forbidden, but as long as the virtual pair annihilates in a time less than h/E, the uncertainty principle allows such fluctuations.

Now, finally, here's a way to understand Hawking radiation. Picture a virtual pair created outside a black hole event horizon. One of the particles will have a positive energy E, the other a negative energy -E, with energy defined in terms of a time coordinate outside the horizon. As long as both particles stay outside the horizon, they have to recombine in a time less than h/E. Suppose, though, that in this time the negative-energy particle crosses the horizon. The criterion for it to continue to exist as a real particle is now that it must have positive energy relative to the timelike coordinate inside the horizon, i.e., that it must be moving radially inward. This can occur regardless of its energy relative to an external time coordinate.

So the black hole can absorb the negative-energy particle from a vacuum fluctuation without violating the uncertainty principle, leaving its positive-energy partner free to escape to infinity. The effect on the energy of the black hole, as seen from the outside (that is, relative to an external timelike coordinate) is that it decreases by an amount equal to the energy carried off to infinity by the positive-energy particle. Total energy is conserved, because it always was, throughout the process -- the net energy of the particle-antiparticle pair was zero.

Note that this doesn't work in the other direction -- you can't have the positive-energy particle cross the horizon and leaves the negative- energy particle stranded outside, since a negative-energy particle can't continue to exist outside the horizon for a time longer than h/E. So the black hole can lose energy to vacuum fluctuations, but it can't gain energy".

 

Edited by beecee
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5 hours ago, Q-reeus said:

 

See above - any analogy to financial ledgers is woefully inadequate.

Applying conservation laws is no different from bookkeeping.

8 hours ago, Q-reeus said:

You also fail to answer my question.

There was no question in the part I was responding to.

8 hours ago, Q-reeus said:

What exactly are the 'particles' or more specifically 'quanta' that get swallowed up?

Any virtual particle.

8 hours ago, Q-reeus said:

Vague hand-waving about 'the BH gives up some energy' just doesn't near cut it.

Then I suggest you look up the journal articles describing it. Which may require you to go to grad school and learn the relevant details, to decipher it.

Meanwhile, turning virtual particles into real ones by adding energy is experimentally confirmed.

https://newatlas.com/scientists-create-real-protons-from-virtual-ones/20689/

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1 hour ago, swansont said:

Applying conservation laws is no different from bookkeeping.

I made it real clear the issue was one of coherent detail, and that bookkeeping is merely an overall constraint that offers no coherent detail.

Quote

Any virtual particle.

Really? Because every particle pair creation process I'm aware of results in two real particles - never one real plus one virtual. Symmetry requirements!

Quote

...Meanwhile, turning virtual particles into real ones by adding energy is experimentally confirmed.

https://newatlas.com/scientists-create-real-protons-from-virtual-ones/20689/

Straw man. I have never suggested otherwise. And to repeat, in all such experiments the created particles in all pairs are both real - never one real plus one virtual.

2 hours ago, Strange said:

To understand the details, you need to look at the math.

Otherwise you have to accept the various analogies as crude sketches of what is going on.

While the math has a reputation for being notoriously difficult, an intelligible physical picture should emerge at the end. We have two standard picture givens - real photons aka HR given off, and a shrinking BH mass accordingly. Just how and what facilitates that shrinkage, in a consistent, believable manner, is what's been my central and unanswered question.
Evidently no-one here has a comprehensive grasp of the detailed HR picture(s)

Given my complete confidence EH's don't and can't exist, the whole HR enterprise is thus imo an elaborate castle in the air.
For that reason and above assessment of complete absence of expertise on standard HR theory at SFN, I will not pursue the matter further here.

Edited by Q-reeus
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11 minutes ago, Q-reeus said:

While the math has a reputation for being notoriously difficult, an intelligible physical picture should emerge at the end. We have two standard picture givens - real photons aka HR given off, and a shrinking BH mass accordingly. Just how and what facilitates that shrinkage, in a consistent, believable manner, is what's been my central and unanswered question.
Evidently no-one here has a comprehensive grasp of the detailed HR picture(s)

I posted a couple of links to articles that attempt to provide more accurate descriptions of how the math works. Hawking's original paper is actually quite readable from what I remember (haven't looked at for many years).

Quote

Given my complete confidence EH's don't and can't exist, the whole HR enterprise is thus imo an elaborate castle in the air.
For that reason and above assessment of complete absence of expertise on standard HR theory at SFN, I will not pursue the matter further here.

Well, it is obvious you believe GR is wrong, but in that case you don't believe that Hawking radiation can exist so why bother asking about the mechanism? Seems a bit pointless. The fact that people here are not able to convince you that these analogies are vaguely plausible certainly isn't evidence against GR.

But as you are unable to show any evidence that GR is wrong your personal beliefs don't really belong n a science forum.

Of course, it may turn out that event horizons don't exist (or at least not in the way that is currently thought) when we eventually have a theory of quantum gravity. Many people are working on such ideas. Hawking himself published a brief paper suggesting that event horizons might be "porous" because of quantum effects. 

It will be very exciting to see how it turns out. But I am not placing place much hope in the personal beliefs of random non-experts on the Internet.

 

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