# Black Hole Entropie and Pair Production

1. Nov 11, 2005

### hossi

Hi All ,

I have a question which is at least partly one of believe but I would be interested in your opinion. We know that there is some problem with the black hole's entropie. If some object with entropy S collapses and it evaporates completely via Hawking Radiation, then where has all the information about the initial state gone? There it is: the information loss problem.

My point of view about this is that the information loss problem can only be solved if the singularity in the inside is avoided. Let us therefore assume that there is no singularity inside the black hole - it is avoided by some unknown quantum gravity effect, but the stuff is dense and stable inside the horizon.

I found that my point of view about the entropy is kind of unusual. Consider, there is some matter which collapses. It has entropie S. This stuff forms a horizon by which the inside region gets completely causally disconnected and with it all information about the initial state. Then, the horizon makes Hawking radiation, which is what we see from the outside. It comes with an entropy S_H, which is what we usually call the entropy of the black hole. In contrast to this, I say, there is more entropy inside, it just can not interact.

http://xxx.lanl.gov/abs/hep-th/0501103" comes with the following argument against this: If the black hole has more information inside, then there are arbitrarily many black holes which look alike from the outside. This would mean that in a pair production process of black holes, the phase space would be arbitrarily large. Which we would not really want it to be.

Besides the fact that I don't really know how I should describe the pair production of black hole's :yuck: , I don't see why this should be the case. Sticking with my point of view, the produced black hole is just a gravitationally extremly strong bound system of particles. But these still have to be particles and should have been produced. Thus, the black hole's phase space would be that of whatever particles could be produced (say, some quark pairs or photons or whatever). You could say, they are still produced, they are just so clumped together that they have a horizon.

Does that make sense? Or have I misunderstood the pair production argument?

Last edited by a moderator: Apr 21, 2017
2. Nov 11, 2005

### hossi

grumpf

entropy entropy entropy entropy, sorry, will repeat that 100 times, Entropie is German entropy entropy ....

3. Nov 12, 2005

### hellfire

Probably I am not going to answer your question, but I would like to understand it. If one identifies the entropy with the area of the horizon, as is usually done, then I would guess that it follows somehow that the possible microstates must be on the area and not in the volume. The phase space of the interior seams to be irrelevant, at least for observers located outside. As far as I know this observation is the motivation for the formulation of the holographic principle: If entropy is an extensive variable, then the volume delimited by the horizon should be replaced by the area as the real physical entity where the degrees of freedom reside. After reading the paper you linked (without understanding it however) I got the impression that this position is more consistent than arguing that there could be also entropy inside the horizon. What I know for sure is that horizons are weird,... but you were asking about pair production?

4. Nov 12, 2005

### rtharbaugh1

I don't understand this stuff either, but I'd like to throw in an idea.

If we are going to discuss the volume of a black hole, there is a problem. There is no gauge symmetry between the outside and the inside of a black hole. In fact, space and time as we experience them get very distorted near the event horizon. How then do you measure distance or time? Imagine asking how many units of volume can fit inside the event horizon. For the sake of a standard, let us imagine that the unit of volume is a marble. How many marbles can fit in a black hole?

The problem is that as the marbles drop into the black hole, they lose their charachtor as marbles. They go through a quantum strainer, become sphagettified, and undergo time dilation as well. Used as a gauge, the marbles inside the hole cannot be compared to the marbles outside the hole. It may very well be that the inside of the hole can hold more marbles than there can be outside. Remember that the marbles get smaller and smaller as they fall further into the hole, like the interlocked devils and angels at the center of an M.C.Escher drawing. Is there any way to count them, or are they uncountable?

So if we try to drop a metered string into a black hole, hoping to plumb its depth, and so calculate its volume from its radius, we are doomed to fail. For one thing, we will have to wait until the end of the universe before the string will get to its destination. Because of the spacetime deformation, the string gets shorter as it descends.

5. Nov 13, 2005

### dubmugga

sorry if I get off topic but i just want to understand one thing...

...it is a question i asked a while back that i didn't get a satisfactory answer to

Is a black hole a one, two, three or four dimensional object ???

...a funnel, a plane, a point, a sphere, is it concave or convex and is it's shape dependent on where you look at it from ???

and what would it's dimensionality and shape be like from the inside looking out if that were possible ???

6. Nov 13, 2005

Staff Emeritus
In MWT they have reduced dimensional pictures of a black hole through time. In a static case it would be a 4-cylinder; a three dimensional ball crossed with the real line for time. But the hole had a history, say the collapse of a star, and it has a future, as it dissipates due to Hawking radiation, so the ball (out to the Schwartzschild radius) would suddenly appear in the past as the start shrank past its SR, and then begin to taper down to nothing.

7. Nov 13, 2005

### Mike2

:rofl:
This goes along with a question I have about Hawking radiation and black hole dissipation. If the event horizon rips apart virtual pariticle pairs so that some escape to become Hawking radiation and the others fall into the black hole, then how can a black hole dissipate if half of those particles are continually falling into it? Wouldn't it continually gain more mass and hence never shrink?

8. Nov 13, 2005

### rtharbaugh1

Hi Mike
a couple things here....one is that the model of virtual pairs getting ripped apart at the horizon has been updated. A better idea perhaps is that there is a quantum uncertainty at the horizon which allows some particles to emerge.
and, IIRC, more mass makes the black hole event horizon smaller, not larger.
Seems to me we really have work to do to overcome our space and time prejudices. I made a beginning by imagining that the past and the future are real places, as solid as Chicago. Time as a landscape, where an imaginary being might be able to move at will from past to future or future to past. Of course we at this writing have no such freedom. We fall through time like a marble falls down a well, and have no volition to turn and go back.
What we do have, by virtue of our immense complexity and continual self-reference, is memory. We have the ability to remember what has just gone by. What is more, or perhaps the same, we have the ability to modify things that are falling with us through time in a way that allows us to communicate ideas to others who are falling....even to others who do not yet exist but may exist in our immediate future.

This ability to remember and communicate requires a certain level and a certain kind of complexity. We generally call this level of complexity consciousness, and the kind of complexity, intelligence.

You and I have some duration in time, but entropy demands that we dissipate. We can create some things that will outlast us. The museums are full of examples of how solid things degrade over time. Best of all we can create ideas, which exist beyond the limits of solid things, and can be reproduced through a wave-like motion of solid things, virtually forever. As long as there are solid things to carry the wave, anyhow.

Information is "like" a wave form in solid things. An encyclopedia carries lots of information. Of course the wave is not in the pages moving up and down or anything like that. It is more easily seen in the rather complex motions of people who pick up the encyclopedia and read or copy it. But information is to some degree less susceptible to the second law. Entropy must have an effect eventually, as information is dependent on material. But to a large extent, compared to the duration of, say, a stone statue covered in gold leaf and protected by a large marble building, information can endure where material cannot. So we know of the statue of Athena which stood for some time on the Acropolis, even though we cannot trace an atom of it today.

It is because information is less susceptible to entropy that we can get much less energy out of it. An encyclopedia falling into a black hole is not likely to have greater effect that an identical book composed of gray pages on which no information is present but the same number of atoms of the same kind do exist. If you burn an encyclopedia you do not get more heat than burning the gray book, and perhaps more to the point, you do not get any more heat from a new encyclopedia than you do from one that has been read, or copied, many times. We see that information of this kind is not directly coupled to entropy.

There remains the question of whether or of how much information is carried at the quantum level. In a sense, the coupling constant itself is a kind of fundamental information. The existance of mass has to be informational. The forces each have a fundamental relationship to spacetime, and that relationship must be informational. I think it is probably this kind of fundamental quantum information, for example of spin states, that is at question on the surface of the event horizon of a black hole. If a partical enters the event horizon of a black hole, does it leave a mark?

We may have to say that it does not leave a mark. Once the spin state dissappears into the event horizon, we have no way to recover the information of what kind of spin state it was. The quantum information is then lost to us forever.

Hawking radiation, and perhaps more importantly to us outside the black hole, Unruh radiation, returns some "information" back to us. A partical appears and we can measure its spin. However we cannot relate that partical that we can measure to any partical within the black hole....its appearance must be totally random. We cannot say that it is "the same" partical that fell into the black hole yesterday or five thousand years ago or at the beginning of our universe.

Black holes do radiate something, and Unruh radiation appears whenever any object moves even slightly. On average, Hawking particals and Unruh particals must cancel each other out. But sometimes, by quantum uncertainty, they do not cancel. Or at least, the cancelation has to be averaged over time, so that in a limited region of the space just outside the event horizon, there may be an uncancelled partical. For a while, at least. It may have some duration, but we know that eventually it will encounter its random opposite.

All the particals of the material universe are like that.

So now we can examine what we mean when we say that a partical is "the same", that is, has duration, from one instant to the next. We see right away that if time is indeed a landscape as I have described that particals do not have identity from one instant to the next. Instead, in time, we see a string of similar particals extended in the landscape of time. These particals in a string are most definately not all the same. Particals retain some definite charachtor over time, but they also have the property of change over time. Let us not imagine anything complex, like say an atom or even the nucleus of an atom, made of many parts, but instead focus on the simplest particals, which so far as we know are unitary and have no discernable parts at all. Electrons. Muons. Nutrinos. Quarks.

In nuclear reactions we explain the changes by saying that quarks can undergo certain changes in color. Of course we are not talking about color as we see it in a sunset. Physicists wanted to be cute and poetic and chose to call a certain property of quarks "color", as a sort of metaphore, but in fact it has nothing whatever to do with the various wavelengths of light.

What we do see is that quarks undergo a structured sort of change, not in an entirely random way, but in a way that we can speak of a quark changing from one color to another color. We can set equations and balance reactions, based on the idea that it is the same quark, only haveing undergone a color change.

Neutrinos are thought to undergo changes also, as they travel through space and endure time.

Consider the time landscape for a single partical, lets say a neutrino. We will imagine it is isolated for the time we want to consider. We could model it by thinking of a string of beads, each bead representing the partical in an instant of time. If we choose our time difference carefully, based on the velocity of the particle, we can make the beads quite discrete, even though we know that there is really an underlying continuum. Think of a marble rolling across a gentle incline under a strobe. If we hold the shutter of a camera open, we can adjust the strobe so that we see the marble each time it has moved one diameter. That is the string of beads. Notice that there isn't any actual material string holding the beads, or marbles together. It is just a trick of the lighting, an adjustment of our consciousness, that allows us to see it displayed in this way.

Now the marble may be black on one side and white on the other. As we see it roll, we see it appear to change, even though we know it is the same marble. So we can relate the marble through successive instants and say that even though it changes, it is the same marble. Can we do this for fundamental particals also?

The fundamental partical moves through Planck space, and the strobe is replaced by the Planck time. Planck space and time are quantized, so that we must think of the movement like the movement of a checker on a game board. It occupies successive positions, not a continuum. Does it make a difference if we replace the checker with a different one? What do we mean when we say that the checker in one space is "the same" as the checker in the adjacent space?

In spacetime, when we say that the partical is the same as it traverses space, what we mean is that it occupies adjacent spaces, the other spaces around it being empty. In spacetime, what we mean by "a partical" is the line of adjacent particals. Clearly the adjacent particals are not really the same. They occupy different spacetimes. We can display them in a row.

Now we must ask what causes particals to appear in a row, that is to have duration, in spacetime? We have the twin examples of Hawking radiation and Unruh radiation, where duration of a partical is due to the random local occurance of particals that for a time do not encounter their random opposite. We may even say that time is created between the occurance of an isolate partner and the occurance of its opposite.

I have written myself out for the moment, and I don't know if I have answered any questions, or if I have made any questions better, by my rambling. I hope that some readers may find some use for this meditation, or that it may inspire further waves in the material consciousness that we inhabit.

Be well,

Richard

Last edited: Nov 13, 2005
9. Nov 13, 2005

### hellfire

In his book "A first course in General Relativity" B. Schutz shows how the mass of the infalling particles may seam to be negative for remote observers under some circumstances. This would explain the mass loss of the black hole for remote observers in terms of pair production.

However, the rigorous derivations I am aware of, do not make use of this picture, but show that two different observers in a Schwarzschild spacetime (free fall and stationary) have a different notions of creation and annihilation operators and therefore different vacua and number operators. This implies that the vacuum for one observer is a state with particles for the other. Such a situation is usual in quantum field theory in curved spacetimes.

The remote observer is stationary, its vacuum is known as Boulware vacuum. It seams that it can be shown that the energy density of fields in the Boulware vacuum is divergent approaching the horizon. Therefore, the correct reference frame to describe the fields is not the stationary one, but the one in free fall. This is called Kruskal vacuum. Calculating the expectation value of the number operator of the stationary observer for the Kruskal vacuum shows that the number of particles is not zero but that there are particles and they are distributed according to a thermal distribution. This is the Hawking radiation.

As far as I know this way to derive Hawking radiation is given in modern text books and lectures, but was not the original one by Hawking. He treated the problem in a similar way than scattering problems in standard QFT, describing the behaviour of modes during gravitational collapse of a star. In light of this derivation, Hawking radiation would be rather field excitations that existed before the collapse but never crossed the horizon.

10. Nov 14, 2005

### Mike2

This would imply an antigravitational field associated with these negative mass particles, right? Have these negative mass particles been observed in the lab?
This sounds exactly the same as saying that the acceleration of a gravitational field has an Unruh effect. The observer at a great distance would be stationary, the oberser in the gravitational field would be free falling.

11. Nov 14, 2005

### hossi

Hi All,

Thanks for your answers, though it seems nothing is answered
First some words about the Hawking radiation @ Mike2 and rtharbaugh1: the notion of negative energies falling onto the black hole has nothing to do with http://arxiv.org/abs/gr-qc/0508013" [Broken]. It arises from the confusing fact that inside the horizon, space and time seem to be interchanged, which makes a perfectly ordinary particle appear to have negative energy when expressed in the asymptotically flat coordinate system. For a local observer, everything seems quite normal.

However, I do not so really like this type of interpretation. Instead, try the following: the horizon is a surface where the vacuum is unstable and where energy of the gravitational field can be converted by a tiny fluctuation into a particle pair. One of the particles escapes, the other falls in. The total energy of the hole is thereby decreased.

@ rtharbaugh1 - since the spacetime is static, I don't think the 3-volume inside the horizon is ill-defined in any regard? But if, that would answer my long standing question how Mary Poppins got the had stand into her bag!

@ hellfire:

As I understand it, the entropy bound FOLLOWS from the assumption that the entropy of the black hole is equal to its area (which means, It need not follow if you believe in my interpretation). Anyway, I could not really see the argument why the microstate should be in the whole interior either, so I can't really help with this. But I think, that the entropy being equal to the area and thereby not scaling with the volume does not mean that the states actually have to be on the surface. Their degrees of freedom just have to be reduced.

Last edited by a moderator: May 2, 2017
12. Nov 19, 2005

### josh1

HI Hossi,

Quantum effects prevent true singularities. In fact, horizons form before gravitational collapse is complete.

A slight technical snafu with the pair creation viewpoint as it’s usually explained is that the uncertainty principle prevents the localization of particles inside the hole within a distance smaller than it's characteristic size, so the idea of particles being created at a specific location, like the event horizon, isn’t accurate.

Another way to describe evaporation is in terms of a particle escaping the hole by tunnelling directly from the singularity, but for related reasons, it’s not any better.

Anyway, theres no one correct way to view this since the particle concept is observer-depenent: The definition of particles is made in terms of mass and spin, these simply labelling representations of the lorentz-group. Since the isometries of flat spacetime are given exactly by the lorentz group, the concept of particle is globally well-defined. But in curved spacetime, physics is only locally lorentz-invariant. For example, the observer hovering above an event horizon will detect hawking emission while an observer in free fall across it wont.

You should look at the recent paper http://xxx.lanl.gov/abs/hep-th/0507171[/URL] by hawking in which he concludes that there’s no information loss involved in black hole physics. Basically he points out that an observer at spatial infinity can’t know whether a black hole forms and including both possibilities produces unitary amplitudes.

In fact, he notes that one can always introduce a negative cosmological constant sufficiently small so as to leave the behaviour of the black hole unaffected. This allows the use of the AdS/CFT correspondence which implies that quantum gravity in spaces with a negative cosmological constant are unitary since they’re dual to CFT’s which are unitary.

Last edited by a moderator: Apr 21, 2017
13. Nov 20, 2005

### Hans de Vries

Last edited by a moderator: Apr 21, 2017
14. Nov 16, 2006

### Demystifier

My point of view seems to be quite similar to yours:
http://arxiv.org/abs/hep-th/0402145
But we already agreed that we have much in common, didn't we? :)

Last edited by a moderator: Apr 22, 2017
15. Nov 16, 2006

### R.X.

As if there wouldn't have been an answer to this old problem since a couple of years. Hawking himself conceded his bet lost, and now agrees with the string people that information is preserved. The point is that the Hawking radiation is not really thermal, but there are subtle correlations encoded in the radiation that carries the information that went in.

16. Nov 16, 2006

### william donnelly

I think this gels nicely with the interpretation of black hole entropy as entanglement entropy. The state outside the horizon has positive entropy, but only so long as you trace over the inside of the horizon. As the horizon gets smaller, you trace out over a smaller region and so you would expect the entropy to decrease until finally you are tracing over nothing and your state becomes pure again.