# Hawking Radiation 2 (different question) (1 Viewer)

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#### Silverious

That last thread was pretty in depth, and I didn't understand alot of it.

But what I got out of it was, a virtual particle pair creates near the EH, one has positive energy one has negative, to satisfy the "ground state" vacuum.

One particle falls in, the other escapes.

So, can't either particle go into the black hole? The positive can go in on one pair, and the negative on another pair.

And if this is true, how can a blackhole ever evaporate? Wouldn't the chance of one going in over the other be 50/50?

#### LURCH

As I stated in the other thread, and this was later confirmed by some with more backgroound than I, the virtual partical pair are only virtual, and the statement as to which of them is the positive and which is the negative cannot be made. However, once one falls into the EH, and the other escapes to become a real particle, this event determines the nature of the two because real particles have positive energy. Therefore, the distinction is made after the VPP has already been generated, at the moment one falls in, that the one that escapes and becomes real must be the positive energy constituant of the pair, and the one that falls in must have been the negative.

Counterintuitive, but it seems to be true.

#### Ambitwistor

"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, thoughout 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."

LURCH is correct: in short, whichever particle falls in becomes the negative-energy particle, by definition.

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But Carlip then says that the erstwhile negative energy particle, upon crossing the horizon, becomes positive energy due to the change of coordinates (radial axis becoming timelike). I seem to remember that the coordinate singularity at the horizen can be "transformed away" by a suitable coordinate transformation. How does this energy switch be the particle survive under such a coordinate transformation? Is it generally covariant?

#### Ambitwistor

But Carlip then says that the erstwhile negative energy particle, upon crossing the horizon, becomes positive energy due to the change of coordinates (radial axis becoming timelike).
Yes, it's negative energy with respect to an external observer, not with respect to an observer inside the horizon.

I seem to remember that the coordinate singularity at the horizen can be "transformed away" by a suitable coordinate transformation. How does this energy switch be the particle survive under such a coordinate transformation? Is it generally covariant?
I'm not sure what you're getting at. You can't detect the presence of a horizon locally. And you can find coordinates in which the horizon isn't a coordinate singularity. But the horizon itself is still there, of course; it has a coordinate-independent definition, and you can't just "transform it away".

On the other hand, coordinates are relevant to determine what an observer sees, since you can adapt coordinates to describe a particular class of observers. Schwarzschild coordinates are adapted to describe what a static observer sees (although you can use them to infer what any other observer sees, by general covariance). An observer falling freely towards the hole won't see Hawking radiation from the hole at all: what are real particles to an outside static observer are virtual to the falling observer.

#### Labguy

One thing that I have noticed, after reading very many pages of info I found on "classical" Hawking Radiation, is that it was conceived, and most often described as in its original form as applying to a static, non-rotating, non-accreting and chargless black hole in the original Schwartzchild configuration as a simple mass-only expression of the Rs. All of the virtual particle pair production scenarios are based on this and require one particle to "fall back" with the other escaping as a real particle causing a mass loss of the BH.

However, many other sites and many past PF Forum threads have noted that it is almost impossible to form a BH with no angular momentum (spin). Even the "no hair" statement was that a BH has only three observable properties; (1) mass, (2) angular momentum and (3) charge (usually net zero). But a lot of recent discoveries (and older theories) have added one new property that is (4) magnetic field. At first, it was thought that a magnetic field would only surround a BH that was accreting matter, but Khanna and Zeldovich has shown that all black holes will have a magnetic field. There is also the term "Hawking Process" appearing which includes/combines the original HR work with work of others as mentioned as well as Thorn and especially Kerr (for spin) and Newman (for charge). The "Kerr-Newman" BH. (A source quote:) “Finkelstein's Black Hole, which shows how Mass curves SpaceTime by Gravity, can be generalized to deal with Spin and Electric Charge. The generalization, called a Kerr-Newman Black Hole, was developed by Kerr (who generalized to add angular momentum J to mass M in 1963) and by Newman (who generalized to add charge e in 1965), according to the book General Relativity, by Robert Wald (Chicago 1984).”

Here are a few sites to peruse with some of the quotes provided. Any emphasis (bold and underline) was added by me to draw attention to particular phrases. Unfornunately for a PF reader, you would have to link to a link to a link and back again to get to the 50-60 points of significance, a long task which wouldn't be expected. Somewhere in this mess is a statement, with mathematical proof I don’t understand, that “A rotating black hole will act, at the event horizon, exactly like a rotating metal sphere.”

http://www.innerx.net/personal/tsmith/BlackHole.html#KerrNewman
"In his paper "Generation and Evolution of Magnetic Fields in the Gravitomagnetic Field of a Kerr Black Hole", Ramon Khanna says: "... a rotating black hole can generate magnetic fields in an initially un-magnetized plasma. In axisymmetry a plasma battery can only generate a toroidal magnetic field, but then the coupling of the gravitomagnetic potential with toroidal magnetic fields generates poloidal magnetic fields. Even an axisymmetric self-excited dynamo is theoretically possible, i.e. Cowling's theorem does not hold close to a Kerr black hole. Due to the joint action of gravitomagnetic battery and gravitomagnetic dynamo source term, a rotating black hole will always be surrounded by poloidal and toroidal magnetic fields (probably of low field strength, though). The gravitomagnetic dynamo source may generate closed poloidal magnetic field structures around the hole, which will influence the efficiency of the Blandford-Znajek mechanism [whereby coupling of the gravitomagnetic potential with a magnetic field results in an electromotive force that drives currents that may extract rotational energy from a black hole.” ….and:

"in June 1971 ... Zeldovich announced a spinning black hole must radiate ... a spinning metal sphere emits electromagnetic radiation ... The radiation is so weak ... that nobody has ever observed it, nor predicted it before. However, it must occur. The metal sphere will radiate when electromagnetic vacuum fluctuations tickle it.. Zeldovich's mechanism by which vacuum fluctuations cause a spinning body to radiate. <His sketch> showed a wave flowing toward a spinning object, skimming around its surface for a while, and then flowing away. The wave might be electromagnetic and the spinning body a metal sphere ... or the wave might be gravitational and the body a black hole. The incoming wave is not a "real" wave ... but rather a vacuum fluctuation. ... the wave's outer parts are in the "radiation zone" while the inner parts are in the "near zone" ... the wave's outer parts move at the speed of light ... its inner parts move more slowly than the body's surface is spinning ... the rapidly spinning body will ... accelerate ...[the inner parts of the incoming wave] ... The acceleration feeds some of the body's spin energy into the wave, amplifying it. The new, amplified portion of the wave is a "real wave" with positive total energy, while the original, unamplified portion remains a vacuum fluctuation with zero total energy. Zeldovich proved that a spinning metal sphere radiates in this way; his proof was based on the laws of quantum electrodynamics.”

"Hawking undertook the task of applying quantum mechanics to black hole dynamics. While his formulation is beyond the scope of this web page, a slightly quantitative and highly qualitative examination of the problem can yield a very good picture of what Hawking discovered. Hawking first attempted to examine the space-time outside the black hole using quantum field theory, which has a very different picture of empty space than the classical definition. His first step was to consider what happens when any field (for example, the electromagnetic field) is quantized in the space-time exterior to a black hole. The quantum mechanical description of a vacuum is space seething with virtual particles and antiparticles whose presence cannot be detected directly." ….. and:

"At first glance, this process of virtual particle creation may seem a little phony. With that in mind, we can consider the more tangible case of electric field particle creation. (This process can actually be observed by applying a strong electric field across a capacitor in a vacuum.)" …. and:

"The quantum mechanical description of the vacuum allows for the creation of the particle/antiparticle pairs, and the electric field tends to separate the charges. If the field is strong enough, the particles tunnel through the quantum barrier and materialize as real particles. The field necessary to accomplish this feat is achieved when the work done to separated the charges by a Compton wavelength equals the energy necessary to create the particles. It should be noted that conservation of energy is not violated, as the energy it took to create the particles would be precisely equal to the decrease in the energy of the weakened electric field.".. (Labguy Note: not necessarily just the BH mass loss.) … and:.. then goes on to explain the process from previous posts where:

“"So far we have not introduced the possibility of a charged black hole, and will only consider an uncharged, non-rotating black hole." <clip> “When looking at the entire system, the total energy of the black hole has decreased and therefore, by Einstein's famous relation, the mass must have decreased. This is the process by which black holes radiate, which is now known as Hawking radiation.”

So, it seems as though "Hawking Radiation" is usually used in this classical, non-rotating and uncharged framework. Another term, maybe "Black Hole Particle Emmissions" would be a better term for the production of PAIRS of REAL particles referred to above. (?)

The last site's sources are:

Wald, Robert M. General Relativity. Chicago: University of Chicago, 1984.

Eisberg, R. and Resnick, R. Quantum Physics. New York: John Wiley & Sons, 1985.

Narlikar, J.V. Introduction to Cosmology. Cambridge: Cambridge University Press, 1993.

Hawking, S.W. Hawking on the Big Bang and Black Holes. New Jersey: World Scientific Publishing Co., 1993.

Hawking, S.W. A Brief History of Time. New York: Bantam Books, 1988.

Shapiro, S. and Teukolsky, S. Black Holes, White Dwarfs, and Neutron Stars - The Physics of Compact Objects. New York: John Wiley & Sons, 1983.

Thorne, Price, and Macdonald, eds. Black Holes: The Membrane Paradigm. New Haven: Yale University Press, 1986.

Wald, Robert M. General Relativity. Chicago: University of Chicago, 1984."

Most of this post is info from Tony Smith's "online book" of 5,000+ pages, last updated 10/06/2003. and NO!; I didn't read it all..

A few more specifics are at:
http://www.innerx.net/personal/tsmith/BlackHole.html
http://www.mpifr-bonn.mpg.de/gcnews/gcnews/Vol.10/rfc@gc.physics.arizona.edu_magfieldsgr.abs.shtml [Broken]
http://xxx.lanl.gov/abs/astro-ph/9903091
http://www.physics.gatech.edu/people/faculty/dfinkelstein.html
http://www.innerx.net/personal/tsmith/d4d5e6hist.html
http://www.innerx.net/personal/tsmith/cdomain.html

Labguy

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#### Ambitwistor

The idea of an event horizon as analogous to a conducting surface is treated in depth in Black Holes: The Membrane Paradigm by Thorne et al.

The radiation process described is the quantum analogue of black hole superradiance, which is itself related to the Penrose energy extraction process in the presence of an ergosphere (cf Wald).

Non-vacuum pair production (i.e., where the pair's nonzero total energy comes from a background field) from black holes is analogous to the ordinary flat spacetime process, although the process is modified when an event horizon is present. I don't know whether there is a separate term for this kind of radiation.

#### Labguy

Originally posted by Ambitwistor
The idea of an event horizon as analogous to a conducting surface is treated in depth in Black Holes: The Membrane Paradigm by Thorne et al.

The radiation process described is the quantum analogue of black hole superradiance, which is itself related to the Penrose energy extraction process in the presence of an ergosphere (cf Wald).

Non-vacuum pair production (i.e., where the pair's nonzero total energy comes from a background field) from black holes is analogous to the ordinary flat spacetime process, although the process is modified when an event horizon is present. I don't know whether there is a separate term for this kind of radiation.
I agree 100%, because somewhere in all that stuff I read was exactly what you just posted. Some pages called it a (one of several) "Hawking Process" and some just as Quantum tunneling. There were also "Hawking-Einstein effect", Hawking-Penrose process" and a few others, but I couldn't figure out which one was referring to that specific effect. The math, of course, put me out in left field, but the verbal explanations wern't too tough so I just posted a bunch of quotes in plain english and some interesting websites to wade through.

#### Labguy

Originally posted by Nommos Prime (Dogon)
http://www.slac.stanford.edu/slac/media-info/20000605/chen.html
Interesting, and another "Hawking effect", but the one I had been trying to remember for so long was the "quantum tunneling" through a strong magnetic field like I posted a (little bit of) above. This Unruh site mentions mostly the "gain" from accelleration, even though one spot does say that "Joseph Rogers of Cornell University proposed that a magnetically confined electron in a so-called Penning trap would give the Unruh signal."

I would guess that there will be more than just a few new proposed Hawking effects to come, and that all may fit the theory, but only a few will actually be observable (later) outside the EH of known, or yet-discovered, "real" black holes. Thanks for the link; I kept it.

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#### ranyart

Great papers spark great debate's,

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#### ranyart

Matt Visser has posted a couple of papers in Pre-print Xarchive, this one in collabaration with D L Wiltshire, relates to the subject we have been looking into:http://uk.arxiv.org/abs/gr-qc/0310107

It has a definate relevance to our recent discussions.

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