this guy seems to have it down pat....


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, 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.

glad thats plain

Thanks Damian. There's some more study I need to do I think before I question some of that info. The sceptic in me is trying to poke holes in it, but that's not really fair until its understood, and there is some new stuff there I need to digest.

Thanks again, I'll chase up those leads and get my head around that first.

Al.

In the Farmersburg School Questions Show, I just heard Fraser say, that if you go fast enough you'll turn into a black hole. Is that really so? I remember reading somewhere before, that speed does NOT really increase the mass of a moving body. Momentum and kinetic energy, yes, but NOT the mass. And that the whole concept of "relativistic mass" is just confusing and not really needed.

So how about it? What say all yous experts here?

EDIT: I'm not again sure if this thread is the right place for this kind of post, but I couldn't find the Farmersburg thread, and it's kinda 'bout black holes anyways...

I happened to find a couple links that say just this:

http://math.ucr.edu/home/baez/physic...lack_fast.html
http://math.ucr.edu/home/baez/physic...y/SR/mass.html

Are these just plain old BS then?

First, I love this podcast! I found it through I-Tunes and now am caught up in just a few days!

But the ideas behind black holes really have me thinking...so here we go:

1 - In most analogies of a black hole, people think of it as a larger vortex bringing things into it. However, that would mean that gravity is working as a vector...in one area and direction of the entire singularity. However, Gravity should be working in all 720 degrees of the singularity. This is kind of like me standing in American and gravity of earth is affecting a person in China the same way. If this is the case, then woulnd't there be a large sphere of bent light all around a black hole? Thus making it a very bright object rather then a very dim object?

2 - One of the basic laws of physics I was taught was that energy/matter can not be created or destroyed...only changed into something else. If a particle is popped into existance by a black hole...what is it created from? Also part of this...it has been described as a particle and anti-particle are created from the black hole...which causes it to evaporate. However, if gravity of a black hole is strong enough to hold light back...wouldn't the particle that escpaped need to go faster then the speed of light in order to do so? If it does not, wouldn't it feed the Black Hole?

1/Dont know

2/the virtual partical pair come into existance just outside the event horizon
one falls in one escapes.....virtual particals are popping into existance everywhere its just near the black hole one steals existance...?

The problem I have with one particle escaping...even at the event horizon...assumes that the particle has some form of velocity in order for it to escape.

I do'nt know if you can create a particle with velocity. First, you would need a lot of energy just to create said particle...then even more energy to move it at the speed of light.

Without moving at the speed of light, the particles would still get sucked into the black hole...meaning one would make it evaporate (the anit-particle) and one would feed it (the particle).

right?

llatpog may be right that most of the escaped virtual particles would be recaptured by a super massive black hole. This may be one of the reasons these produce very litle Hawkings radiation and micro black holes (if there are any) produce huge amounts of Hawkings radiation. Micro black holes would rarely succeed in capturing anything because they are so tiny. Neil

Yet another black hole question,

If it were possible to divide a black hole in half, and those halves were then below the minimum threshold to create a black hole, would all the matter or energy suddenly be released? (reasoning the gravity no longer being strong enough). If fear I have some error of understanding about the nature of the singularity i.e. once created the mass in no longer critical.

__________________
“Life is not measured by the number of breaths we take, but by the moments that take our breath away”

In the following, I provide responses to questions and statements by several conributors to this thread. Each paragraph begins with the name of the contributor to whom that paragraph is applicable. Paragraphs not introduced by a name are continuations of the previous paragraph.

moriankey: The energy consumed in creating a particle pair outside a black hole must necessarily have been borrowed temporarily from the space in which the particles appear because it cannot have passed through the event horizon to arrive there. The process must begin with production of a pair of particles OUTSIDE the black hole, one particle then falling into the black hole and the other remaining outside with enough kinetic energy to prevent it from falling into the black hole. When it first appears, it must already be moving away from the black hole fast enough to escape to infinity.o

Chas: Space will not spin. It will be twisted in the direction of rotation of the black hole by an amount determined by the mass of the black hole and its rotationial velocity. The phenomenon is called "frame dragging".

Mrs. B: "Quark soup" is the name given to the contents of the Universe immediately after quarks, mesons, electrons, and other esoteric particles, comprising a plasma, condense out of the nearly pure radiaton comprising the contents of the Universe during the first moments of the Big Bang.

Hawkinns and Thorne had a bet on whether matter could escape from a black hole. Hawkins later devised the mechanism, involving "Hawkings radiation" that explained how matter COULD escape a black hole, thereby proving himself wrong and losing the bet.

namcitsym: There is no limit to how much matter can fall into a black hole.

Maddad: A person unfortunate enough to fall into a black hole would experience no local slowing of local time, that is how fast his clock ran, as he approached and fell into the black hole. However, he would see time at locations remote from his own location speeding up faster and faster as he approached the event horizon. He'd notice nothing whatever to tell him when he passed through the event horizon. Observers outside the event horizon would never see him pass through the event horizon for it would appear them that time he was going slower and slower as he approached the event horizon. In fact, it would appear to them that he never reached the event horizon, much less passed through it.

bons212: Objects are drawn into black holes from all directions.

Evileye: The way that objects fall into black holes is more like the way comets come into the solar system than the way planets orbit the sun in roughly coplanar orbits. General relativistic frame dragging will tend to pull them into the plane of the black hole's rotation, also collisions between orbiting objects will tend to bring them into the rotational plane of the black hole.

Uranu5: "a gravitational pull = to the speed of light" is like comparing monkeys and trees. Gravitational pull is force. The speed of light is a speed, There is no way to compare force with speed. The rotation of a black hole has nothing to do with its gravitational effects although its rotation can affect its gravitational effect through general relativistic frame dragging. A black hole does not "pull in other matter from different parts of the body of the mass creating the black hole which makes the pulled in material move towards the points that are moving across the equater."

sheeny: The mechanism of evaporation from a black hole involves quantum-mechanical "tunneling". In classical mechanics, nothing can escape from a black hole. The contents of a black hole can be seen as a collection of particles in thermodynamic equilibrium, the most energetic particles falling just short of having enough energy to escape from the black hole. In quantum mechanics, particles can "borrow" energy from the vacuum but must return it after a brief time, but that time is long enough so that the borrowed energy enables them to pass throuugh the event horizon. Through this mechanism, a few photons, neutrinos, electrons,and a few more massive particles can occasionally escape from the black hole. The photons appear outside the event horizon as blackbody radiation at a temperatuure only a degree or so above absolute zero. There's also the model that you described. But the model involving tunneling seems closer to what actually happens. As you stated, evidence for the existence of Hawking radiation has yet to be found.

I think, as I understand it, the energy for Hawking's radiation ultimately comes from the mass of the black hole. That is why it is thought that a smaller black hole would shrink and finally explode as it no longer has enough mass to accelerate stuff to C. The paradox is one particle of the pair escapes and one enters the event horizon, yet the black hole loses mass (equal to the mass times velocity of the escaped particle. I don't understand why).

Hawking's radiation may have been observed in collisions between gold nuclei at the Relativistic Heavy Ion Collider (RHIC) . I do not understand this article by Dr. Horatiu Nastase enough to determine this. Work from the Large Hadron Collider (LHC) should shed more light on this subject, in the next year or so, maybe.

It is a great time for astrophysics!

__________________
I admit it. I AM obsessed with the RHIC. Hey, what u gonna do while you are waiting for the LHC?

I'll offer answers and responses to some of the questions and comments raised by contributors to this thread. Each begins with the pseudonym of the contributor of the question or comment followed by the question or comment, followed by ":--", and, starting on the next line, my answer or comment.

jwswitzer: It was mentioned that smaller black holes can vaporize. The analogy was that a glass of water, if left for a time, will vaporize and the water will disappear. However, the water really just changes form from a liquid to a gas. If I understand correctly the laws of physics require the vaporized black hole to not "disappear", but to also change into something else. Just what does it change in to?:--

All black holes evaporate, not just small ones. But only small ones evaporate fast enough for the evaporation rate to be appreciable. Black holes are believed to evaporate through a quantum mechanical procress that involving pairs of conjugate particles such as electrons and positrons. There is no good description in terms of classical physics. It involves "borrowing" energy from the vacuum, that is, from space itself, just outside the event horizon of a black hole subject to the requirement that the energy be returned to the vacuum within a time prescribed by the uncertainty principle of quantum mechanics. The process has been pictured as spontaneous creation a pair of conjugate particles such as electrons and positrons from vacuum energy just outside the event horizon, one of the particles then falling through the event horizon while the other acquires enough energy through its fall into the black hole to repay the borrowed energy, The substance of the vaporized black hole is passed into the escaping particles. The actual process is much more complicated, involving quantum field theory.

PhilM: If you have these particle pairs that are randomly being generated where one goes into the black hole and the other isn't, how does it evaporate if it is still consuming particles?:--

See my answer to jwswitzer's question.

morlanky: When matter gets sucked into a black hole, it gets converted into energy. When Hawking radiation occurs, the energy gets transformed into matter again and gets spat out. Make sense?:--

Matter falling into a black hole is not converted into energy: It contributs to the mass of the black hole. The matter falling into the black hole is not converted into energy via black-hole evaporation. See my answer to jwswitzer's question.

The black hole is, in a sense, consuming negative calories. In return, it's spitting out positive, not negative, calories.

Himanshu Raj: Why do they (massive particles) have to go round the massive object before falling into it instead of going straight into it? How does the law of the conservation of angular momentum apply?:--

Strictly speaking, particles do NOT need to go around the massive object before falling into it. Infalling objects are extremly unlikely to be headed directly toward the massive object. No matter how small the anglke it's heading if off center, its inbound path will be put it on a heading that would take around the center of the massive body. If this path intercepts the massive object's surface, in the case of a black hole its accrettion disk or its event horizon, it will fall in. The law of conservation of angulart momentum is what insures that the above will happen.

Chas: I wrote them out as a MS Word file, but, understandably, the site won't let me attach a doc to a thread post. If anyone is interested in checking my numbers, e-mail me, and I'll be happy to send it to you:--

Perhaps you cannot attach a Word file, but you can copy it into your response, although you'll find that you'll have a limited character set: no bolds, italics, or underscores, superscripts, or subscripts, and limited if any special characters such as integral signs. My comments are copied from Word files.

Black holes, like everytthing else, almost certainly spit, although there is no requirement that they MUST spin. It would be extremely unusual to find one that was NOT spinning. General relativitistic frame dragging would deflect the path of an infalling object if it was headed directly toward the center of the black hole. An appropriate deviation of its path would still allow it to fall directly into the black hole.

Mrs B: What is quarksoup?:--

Quark soup is the name given to the contents of the Big Bang universe immediately after quarks, electrons, and a few antiparticles condensed out of the primordial pure electromagnetic radiation constituing the the Universe during the Planck era preceding 10 exp -43 seconds, the brief interval of the Big Bang history not accessible to model particle physics.

namcitsym: Is there a limit as to how much matter can be consumed by a black hole or will it devour any and all comers across the event horizon? If there is a limit, how is it quantified?

Theory knows of no limit on how large and massive a black hole can become.

Maddad: Time slows for a person approaching the event horizon, and stops when he gets there, but only from the point of view of the outside observer. From the point of view of the inbound traveler, his time is completely normal. Instead of stopping, he squirts right on through. If the black hole is massive enough, he might not even be aware that he had passed the event horizon.

On the other hand, his perceives the outside observer’s time as going faster. When the traveler reaches the event horizon, he would see the outside observer experience all the time through the end of infinity.

What I had hoped to see Dr. Pamela explain was the meaning of time from the point of view of the inbound traveler inside the event horizon in explaining the outside observer. This time must be greater than infinity, which I have difficulty understanding.:--

Your understanding of temporal phenomena associated with black holes is correct. Because the radial and temporal components of the Schwarzschild metric switch roles inside the event horizon, I wouldn't want to predict what the unfortunate traveller would experience before he, she, or it was torn apart by tidal forces, as would certainly happen no matter whatever the size of the black hole.

bones212: It seems to me that the gravity is equal all around it and objects should be drawn from all directions?:--

Correct except for the effect of general relatavistic frame dragging, that would deflect paths toward orbits around the rotational axis of the black hole.

Evileye: Black holes are like any other massive body. They spin. There is an equator, and poles.... sort of. Anything that gets close enough begins to follow the rest of the stuff falling in or rotating around it, much like the rings around Saturn. When they finally pass the event horizon they are no longer visible to us. So the only way to show it on a 2d piece of paper is like a toilet bowl swirl. The stuff doesn't get sucked in from every direction although it may have came that way.

Try to imagine merging into traffic. You were going north, and merge into an eastbound lane. You adjust, the eastbound traffic doesn't.:--

Your description is correct for movement outside the event horizon. Because of the exchanged roles of time and radial distance inside the event horizon, the picture is much more complicated and is not readily described.

publiusr: If you throw a rock into a pond what you get back are the ripples. It can't actually leave the black hole--but it will (for lack of a better word) displace its worth in Hawking radiation.:--

A black hole emits radiation steadily even nothing if falling into it.

omar: My question is, how the super massive black hole is formed? and what had feeded it during it's formation?:--

It forms by accretion of matter from its surroundings, the galaxy in whose center it is embedded. It's fed mostly by stars but also by gas, mostly hydrogen, and dust.

omar: What are the assumptions that underpin Hawking Radiation?:--

See my response to jwswitzer's question near the beginning of this thread.

glad someone knows it all

This is my second batch of answers to questions asked by contributors to this thread. Each answer starts with the contributor's pseudonym, followed by his question, followed by ":--", then my response starting on a new line following a blank line. Responses start following the last entry in my previous list.

sheeny: I'm struggling to understand how the mechanism described for Hawking Radiation results in the black hole evaporating. What are the assumptions that underpin Hawking Radiation?

Your understanding is of the mechanism of Hawking radiation is essentially correct aside from the reservation concerning quantum field theory stated in my response to jwswitzer's question in my previous contribution to this thread. Hawking radiation should appear outside the black hole whether annihilation occured inside or outside the event horizon. If it occurred inside the event horizon, collision of the escaping particle with other particles would constitute the Hawking radiation. If it occurred outside the event horizon, the annihilateion energy itself would constitute the Hawking radiation To date, Hawking radiation has not been observed.

damian1727: As I understand it it does not matter which partical goes in and which escapes....the energy for the ''free'' partical has to come from somplace and that place is the black hole ...so it slowly evaporates. [Answering llatpog] the virtual partical pair come into existance just outside the event horizon one falls in one escapes.....virtual particals are popping into existance everywhere its just near the black hole one steals existance...?... glad someone knows it all:--

Correct, He complimented me by saying, "This guy seems to have it down pat." I can say the same for him.and then some! I doubt that anyone knows it all,

NHR+: I just heard Fraser say that if you go fast enough you'll turn into a black hole. Is that really so? I remember reading somewhere before, that speed does NOT really increase the mass of a moving body. Momentum and kinetic energy, yes, but NOT the mass. And that the whole concept of "relativistic mass" is just confusing and not really needed.:--

Everything Fraser is quoted as having said is totally untrue. The following statements are true:
No matter how fast you go, you will NOT turn into a black hole. Your mass WILL become infinite as seen by stationary observers as your speed approaches the speed of light. As seen by them, you will be moving very close to the speed of light, and your speed as seen by them will change negligibly whether you use energy trying to accelerate or to slow down. The concept of mass in special relativity is indeed confusing, bugt that does not eliminate need for it.

If the links you cited support the above quoted statements, their contents, too, are nonsense. There are lot's of people whose favorite pasttimes seem to be trying to debunk Einstein. So far, Einstein's relativities, both special and general, have stood up under the most rigorous testing. Your response to llatpog regarding appearance of particles outside the event horizon is correct.

llatpog: In most analogies of a black hole, people think of it as a larger vortex bringing things into it. However, that would mean that gravity is working as a vector. If a particle is popped into existance by a black hole...what is it created from? if gravity of a black hole is strong enough to hold light back...wouldn't the particle that escpaped need to go faster then the speed of light in order to do so? If it does not, wouldn't it feed the Black Hole?

The cited analogs are nonsense. Black holes are spherical, not circular, the fact that a nonrotating black hole would be a rarity notwithstanding. Black holes are black because they do not emit any sort of radiation whatever other than Hawking radiation, which has yet to be observed. Particles do not "pop" into existence from black holes. Only Hawking radiation is thought to be able to appear to come out of a black hole. Particles never emerge from black holes. The only way for a particle to appear emerging from a black hole is for the observer to see a particle appear just outside the event horizon and not notice that an antipartice appeared there at the same time.

neilzero: llatpog may be right that most of the escaped virtual particles would be recaptured by a super massive black hole. This may be one of the reasons these produce very litle Hawkings radiation and micro black holes (if there are any) produce huge amounts of Hawkings radiation. Micro black holes would rarely succeed in capturing anything because they are so tiny.:--

llatpog IS right on all counts,

4tune8chance: If it were possible to divide a black hole in half,...:--

It's hard to say what would happen. Theory does not cover that possibility.

Vanamonde: as I understand it, the energy for Hawking's radiation ultimately comes from the mass of the black hole. That is why it is thought that a smaller black hole would shrink and finally explode as it no longer has enough mass to accelerate stuff to C.:--

A small black hole does not accelerate anything to the speed of light., It is only via Hawking radiation that a smaller black hole is expected to finally explode.

Are you sure? Even if it very small, if a particle enters it's gravity well, it will be accelerated. After all the very definition of a black hole is a gravity well that has an escape velocity greater than the speed of light. Typically, a body will accelerate a smaller falling body to or near it's escape velocity unless it has a vector in a different direction. The return of the Apollo spacecraft is an example in the macroworld as they were close to the Earth's escape velocity when they re-entered the atmosphere.

Is this not true, even on the very small scale? Now, I imagine that a capture virtual particle of the pair that leds to Hawking radiation will not be so accelerated as musch it "cheats" by coming into existence so close to the Schwarzschild radius.

Even the effect of the Earth's gravity has been measured on neutrons -
this is not the article I read on it in Scientific American but is yet another example, one that is online.

__________________
I admit it. I AM obsessed with the RHIC. Hey, what u gonna do while you are waiting for the LHC?

dcl where did copy your original pat post from i cant remember?

thanks 4 the input