Hey guys I have a question about Hawking Radiation - How does it escape a black hole? Because you have to exceed c in order to achieve escape velocity, but that's not physically possible... so I guess what I'm looking for is a 2-fold answer the first part being very simple, the second showing the math.

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Originally Posted by spratleyj
Hey guys I have a question about Hawking Radiation - How does it escape a black hole? Because you have to exceed c in order to achieve escape velocity, but that's not physically possible... so I guess what I'm looking for is a 2-fold answer the first part being very simple, the second showing the math.
HR isn't emitted from within a black hole. It is a pair of virtual particles created outside the point of no return known as the event horizon where one particle falls into the black hole while the other escapes.

3. Originally Posted by Lepton
HR isn't emitted from within a black hole. It is a pair of virtual particles created outside the point of no return known as the event horizon where one particle falls into the black hole while the other escapes.
I read the wikipedia page and it was a bit confusing, what I don't get is how a black hole loses mass, if it can only emit what it sucks in...

4. Spratley,
No offense to Lepton, but go to the Horse's Mouth.
Hawking's "Brief History", Chapter 7 "Black holes ain't so black", about halfway through (page 106 in my first edition). He explains, in non-technical terms, his theory of black hole decay.
OR his own website: http://www.hawking.org.uk/lectures/dice2.html
Read the whole lecture, or eif you are desperate start at para 5.
JOhn

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Originally Posted by spratleyj
I read the wikipedia page and it was a bit confusing, what I don't get is how a black hole loses mass, if it can only emit what it sucks in...
The energy to create the particles is drawn from the black hole.

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Originally Posted by spratleyj
I read the wikipedia page and it was a bit confusing, what I don't get is how a black hole loses mass, if it can only emit what it sucks in...
Through QFT, two virtual particles can pop into existance and the annihilate each other, to pop back out of existance. How long those two virtual particles are allowed to pop into existance is dependent on their mass, and determined by the uncertainty principle. Those particles "borrow" energy to become real, then give it back when they annihilate each other. Look up virtual pair production.

Now think of the two virtual particles popping into existance near the Event Horizon. Normally, those would pop back out of existance and nothing would change. However, if the particle pair is close enough to the Event Horizon, Tidal Gravity can force them apart, one falling in, one escaping. Since they don't annihilate each other, the energy to create them has to come from somewhere. That somewhere is the energy of the gravitational field of the Black Hole. Since Energy and mass are the same (E = mc2, the particle escaping takes mass away from the Black Hole.

The whole problem with this is that it really requires a full version of Quantum Gravity. Hawking Radiation is a result of the partial combining of GR and QFT, achieved by Hawking.

7. Originally Posted by Lepton
The energy to create the particles is drawn from the black hole.
Cool, I never know that... so a black hole has the ability to "create" particles? Also...
1) the Hawking "lecture" and the wiki page both said that quantum mechanics causes these particles to be "created" is there somewhere I could look at the mathematics?
2) The wiki page mentions that the particles must have negative energy, how is that possible and why is that necessary?

Thanks for all the responses!

EDIT:

After posting I read Tensor's post, which was good (it seem to be identical to what Hawking says in his lecture)... two more follow questions would be 1) these particles that pop in and out of existence - what energy is used to create them when they don't appear in a black hole? 2) So are you saying that the black hole doesn't really "create" the particles, but that it just supplies the necessary energy?
Last edited by spratleyj; 2008-Sep-28 at 10:52 PM. Reason: tensor's posts

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The negative energy is just book-keeping. If you fell alongside one of these particles on its way into the black hole, it would be just an ordinary particle with the standard rest mass.
Energy is frame dependent (it depends where you are and how you're moving), and we agree conventional values for "zero energy". If a particle has less energy than the conventional zero in your reference frame, it has negative energy; just like map contours around the Dead Sea are marked with negative heights, because they are below sea level.

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Originally Posted by spratleyj
After posting I read Tensor's post, which was good (it seem to be identical to what Hawking says in his lecture)... two more follow questions would be 1) these particles that pop in and out of existence - what energy is used to create them when they don't appear in a black hole? 2) So are you saying that the black hole doesn't really "create" the particles, but that it just supplies the necessary energy?
The energy for the virtual particles is "borrowed" under the terms of the Uncertainty Principle: they can exist only for a period of time that's inversely proportional to their energy, and then they annihilate and disappear. That's going on everywhere, all the time. The black hole's tidal gravity does work on these particles, moving them apart, and manages to deliver enough energy to "promote" the virtual particles to reality, before the limiting time period allowed by Heisenberg comes to an end.
Stronger tidal gravity means more energy delivered in a shorter time, so small black holes can "promote" more energetic particles, and therefore produce more energetic Hawking radiation.

Grant Hutchison

10. Originally Posted by grant hutchison
The energy for the virtual particles is "borrowed" under the terms of the Uncertainty Principle: they can exist only for a period of time that's inversely proportional to their energy, and then they annihilate and disappear. That's going on everywhere, all the time. The black hole's tidal gravity does work on these particles, moving them apart, and manages to deliver enough energy to "promote" the virtual particles to reality, before the limiting time period allowed by Heisenberg comes to an end.
Stronger tidal gravity means more energy delivered in a shorter time, so small black holes can "promote" more energetic particles, and therefore produce more energetic Hawking radiation.

Grant Hutchison

11. Is it true that ordinary matter, as in planets etc, also produces these paired particles...just that there isn't the black hole situation to seperate the two?

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Originally Posted by Frog march
Is it true that ordinary matter, as in planets etc, also produces these paired particles...just that there isn't the black hole situation to seperate the two?
Matter does not produce thesse pairs, they are produced everywhere according to QFT. They can be produced far from anything.

13. See, the virtual pair take out an energy mortgage to fund their existence, with the promise to pay it off when the two shortly recombine and annihilate. When one of them goes fickle and wanders off, failing to fulfil their joint commitment, then the black hole takes in the partner left behind, and pays off the bad debt in an awesome cosmic bailout.

In the end, the blackhole itself runs out of resources to cover the enormous number of instances of such bad debt and must go out of business.

It was doomed from the start.

14. Originally Posted by Tensor
Matter does not produce thesse pairs, they are produced everywhere according to QFT. They can be produced far from anything.
so is ordinary matter just an extension of this?

like the matter that makes up a table is just virtual particle pairs coming in and out of existence, but at a greater rate, due to the higher probability, and proximity?

Is this what a wave function is sort of made of?

or is that ATM?

15. Originally Posted by 01101001
See, the virtual pair take out an energy mortgage to fund their existence, with the promise to pay it off when the two shortly recombine and annihilate. When one of them goes fickle and wanders off, failing to fulfil their joint commitment, then the black hole takes in the partner left behind, and pays off the bad debt in an awesome cosmic bailout.

In the end, the blackhole itself runs out of resources to cover the enormous number of instances of such bad debt and must go out of business.

It was doomed from the start.
Nice analogy

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Dr. Hawking proposed several posible mechanics for evaporation[8]. Many physicists either support or refute the conclusion but very few actually support Dr. Hawking's mechanics. (Dr. Higgs says of Dr. Hawking's particle physics work "he puts together theories in particle physics with gravity . . . in a way which no theoretical particle physicist would believe is the correct theory. " "I am very doubtful about his calculations"[9]). Some physicists conclude that quantum effects may actually cause black hole growth (reverse Hawking Radiation).

Dr. William Unruh (Unruh Effect) supports mBH evaporation but refutes Dr. Hawking's arguments stating "The derivation by Hawking is nonsense, in that it uses features of the theory in regimes where we know the theory is wrong."

Some physicists including CERN's Dr. Ellis support Dr. Hawking's arguments apparently including Dr. Hawking's time reversal conjecture and argue it is a reason we should not fear micro black hole creation.[2][8]

Other physicists published papers concluding that black holes do not radiate.

"black holes do not radiate" Helfer[3]

"…the effect [Hawking Radiation] does not exist." Belinski[4]

"infinitely delayed, too, and hence ceases to be physically effective" Rössler[5]

"it is possible that in a higher dimensional bulk D > 5, the behaviour of the black holes is stable". Maia & Monte[6]

"whether real black holes emit Hawking radiation or not remains an open question" Unruh & Schützhold[7]

[1] http://www.perimeterinstitute.ca/Eve...ity/Abstracts/ Effective Models of Quantum Gravity/Abstracts, W. Unruh

[2] http://cdsweb.cern.ch/record/1120625/ The LHC is safe, Jonathan R. Ellis, CERN (14 August 2008)

[4] http://arxiv.org/abs/gr-qc/0607137 On the existence of black hole evaporation yet again On the existence of black hole evaporation yet again - VA Belinski Paper.

[5] http://www.wissensnavigator.com/docu...IBLACKHOLE.pdf Abraham-Solution to Schwarzschild Metric Implies That CERN Miniblack Holes Pose a Planetary Risk - Otto E. Roessler Theory a

[6] http://arxiv.org/abs/0808.2631 On the Stability of Black Holes at the LHC, M. D. Maia, E. M. Monte (19 Aug 2008)

[7] http://arxiv.org/abs/gr-qc/0408009 On the Universality of the Hawking Effect Unruh and Schützhold (2005)

[8] http://projecteuclid.org/DPubS/Repos...cmp/1103899181, Particle Creation by Black Holes, S. W. Hawking (12 Apr 1975)

[9] http://www.timesonline.co.uk/tol/new...cle4727894.ece Peter Higgs launches attack against Nobel rival Stephen Hawking, TimesOnLine (Sep 11, 2008)

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Originally Posted by Frog march
so is ordinary matter just an extension of this?

like the matter that makes up a table is just virtual particle pairs coming in and out of existence, but at a greater rate, due to the higher probability, and proximity?

Is this what a wave function is sort of made of?

or is that ATM?
No, regular matter is regular matter. You really should check out virtual particles The particles that make up normal matter (such as that table) are real particles. The ones that flash in and out are virtual particles.

18. Originally Posted by JTankers
Dr. Hawking proposed several posible mechanics for evaporation[8]. Many physicists either support or refute the conclusion but very few actually support Dr. Hawking's mechanics. (Dr. Higgs says of Dr. Hawking's particle physics work "he puts together theories in particle physics with gravity . . . in a way which no theoretical particle physicist would believe is the correct theory. " "I am very doubtful about his calculations"[9]). Some physicists conclude that quantum effects may actually cause black hole growth (reverse Hawking Radiation).

Dr. William Unruh (Unruh Effect) supports mBH evaporation but refutes Dr. Hawking's arguments stating "The derivation by Hawking is nonsense, in that it uses features of the theory in regimes where we know the theory is wrong."

Some physicists including CERN's Dr. Ellis support Dr. Hawking's arguments apparently including Dr. Hawking's time reversal conjecture and argue it is a reason we should not fear micro black hole creation.[2][8]

Other physicists published papers concluding that black holes do not radiate.

"black holes do not radiate" Helfer[3]

"…the effect [Hawking Radiation] does not exist." Belinski[4]

"infinitely delayed, too, and hence ceases to be physically effective" Rössler[5]

"it is possible that in a higher dimensional bulk D > 5, the behaviour of the black holes is stable". Maia & Monte[6]

"whether real black holes emit Hawking radiation or not remains an open question" Unruh & Schützhold[7]

[1] http://www.perimeterinstitute.ca/Eve...ity/Abstracts/ Effective Models of Quantum Gravity/Abstracts, W. Unruh

[2] http://cdsweb.cern.ch/record/1120625/ The LHC is safe, Jonathan R. Ellis, CERN (14 August 2008)

[4] http://arxiv.org/abs/gr-qc/0607137 On the existence of black hole evaporation yet again On the existence of black hole evaporation yet again - VA Belinski Paper.

[5] http://www.wissensnavigator.com/docu...IBLACKHOLE.pdf Abraham-Solution to Schwarzschild Metric Implies That CERN Miniblack Holes Pose a Planetary Risk - Otto E. Roessler Theory a

[6] http://arxiv.org/abs/0808.2631 On the Stability of Black Holes at the LHC, M. D. Maia, E. M. Monte (19 Aug 2008)

[7] http://arxiv.org/abs/gr-qc/0408009 On the Universality of the Hawking Effect Unruh and Schützhold (2005)

[8] http://projecteuclid.org/DPubS/Repos...cmp/1103899181, Particle Creation by Black Holes, S. W. Hawking (12 Apr 1975)

[9] http://www.timesonline.co.uk/tol/new...cle4727894.ece Peter Higgs launches attack against Nobel rival Stephen Hawking, TimesOnLine (Sep 11, 2008)

You may have concerns about Hawking radiation and the LHC, but this isn't the place for them, please stop trying to hijack this thread.

On another note since these particles are "created" randomly how can we figure out the time it will take a black hole to evaporate?

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Originally Posted by spratleyj
You may have concerns about Hawking radiation and the LHC, but this isn't the place for them, please stop trying to hijack this thread.

On another note since these particles are "created" randomly how can we figure out the time it will take a black hole to evaporate?
The time to evaporate is given by the equation

tev = (5120*Pi*G2*M3)/(hbar*c4)

ETA - HR is essentially thermal radiation so in order for a black hole to evaporate it's temperature must be lower than the CBR. As a black hole gets smaller, the temperature gets extremely hot.

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Originally Posted by spratleyj
You may have concerns about Hawking radiation and the LHC, but this isn't the place for them, please stop trying to hijack this thread.

On another note since these particles are "created" randomly how can we figure out the time it will take a black hole to evaporate?
They may be created randomly, but we can calculate the rate through either Bose-Einstein or Fermi-Dirac Statistics. The strength of the tidal gravity is dependent on the mass. Counter-intuitively, the smaller the mass, the stronger the tidal gravity. As a result, the rate of radiation is dependent on the Black Holes mass. The smaller the mass, the more radiation.

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Originally Posted by Tensor
As a result, the rate of radiation is dependent on the Black Holes mass. The smaller the mass, the more radiation.
heh...can't we also say the HR is dependent on the temperature as in the higher the temperature the more radiation?

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Originally Posted by Lepton
heh...can't we also say the HR is dependent on the temperature as in the higher the temperature the more radiation?
Actually, no. Since a black hole doesn't have a temperature, the radiation is dependent on the mass.

You may be thinking of the comparisons for thermodynamics and Black Hole thermodynamics. Simplified, for black hole thermodynamics, the surface gravity is the analog to temperature in regular thermodynamics (much as the horizon area is analogous to entropy).

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Originally Posted by JTankers
Many physicists either support or refute the conclusion ...
To "refute" means to prove false by argument. No-one has refuted Hawking's conclusions. I think you may mean that some people disagree with him.

Grant Hutchison

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Originally Posted by Tensor
Actually, no. Since a black hole doesn't have a temperature, the radiation is dependent on the mass.

You may be thinking of the comparisons for thermodynamics and Black Hole thermodynamics. Simplified, for black hole thermodynamics, the surface gravity is the analog to temperature in regular thermodynamics (much as the horizon area is analogous to entropy).
So HR isn't blackbody radiation? That would mean many physicists and cosmologists are wrong.

25. Originally Posted by Lepton
So HR isn't blackbody radiation? That would mean many physicists and cosmologists are wrong.
Have physicists and cosmologists argued that Hawking radiation is blackbody radiation? I always have been under the impression that it is in theory a very different beast.

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Originally Posted by Hornblower
Have physicists and cosmologists argued that Hawking radiation is blackbody radiation? I always have been under the impression that it is in theory a very different beast.
Yes, people have said it is a type of thermal black body radiation and the temperature of black holes can be calculated so I really don't have any idea what Tensor is saying when he claims black holes have no temperature. In any event, it definitely isn't a mainstream view.

ETA - A fairly good approximation of the temperature is given by

T = 0.00000006/MBH in SM

27. Any object which is radiating energy from a surface can be said to have an "effective temperature" equal to the actual temperature of a blackbody that is emitting the same amount of power per unit surface area. That does not necessarily mean that the object in question is a true blackbody, or that it even radiates by the same mechanism as a familiar incandescent body. I have no quarrel with attributing an effective temperature to a black hole.

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Originally Posted by Hornblower
Any object which is radiating energy from a surface can be said to have an "effective temperature" equal to the actual temperature of a blackbody that is emitting the same amount of power per unit surface area. That does not necessarily mean that the object in question is a true blackbody, or that it even radiates by the same mechanism as a familiar incandescent body. I have no quarrel with attributing an effective temperature to a black hole.
However saying it is effective and not a real temperature is wrong and it is definitely not mainstream.

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Originally Posted by Lepton
However saying it is effective and not a real temperature is wrong and it is definitely not mainstream.
And yet an observer who falls freely into a black hole will see no hot region as she falls: just the usual seething of virtual particles all the way through the event horizon.
Only a stationary observer detects thermal radiation; and the deeper they descend towards the black hole's event horizon, the hotter that thermal radiation gets.

So this certainly doesn't seem to operate the way "temperature" conventionally does.

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Originally Posted by Lepton
Yes, people have said it is a type of thermal black body radiation and the temperature of black holes can be calculated so I really don't have any idea what Tensor is saying when he claims black holes have no temperature. In any event, it definitely isn't a mainstream view.
Yes it is. You need to look at the four laws of Black Hole Mechanics. No where in those four laws will you find a reference to temperature. You can calculate a temperature, using the HR. By analogy to the Laws of Thermodynamics, the surface gravity of the black hole (the zeroth law of black hole mechanics) is analogous to the temperature of an object at equilibrium (the zeroth law of Thermodynamics).

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