Is it possible that black holes do not exist?

[rjbeery]

Please correct this if a widely accepted answer exists; please forgive my layman's terminology; lastly, forgive me for posting this to two forums but my first attempt got no takers...

The "infinite" (unaffected by the local gravity effects) observer A knows that a rocket ship carrying passenger B is rapidly approaching the event horizon of a black hole* large enough to have negligible tidal forces in that region. Observer A calculates that passenger B shall cross the event horizon at t = infinity. The typical response to this is that, from B's frame, time passes normally and the cross-over of the event horizon is rather uneventful**.

HOWEVER (again from A's perspective) the black hole will dissipate due to Hawking radiation in a very, very long (albeit FINITE) amount of time. This means that passenger B's material structure will be calculated to be annihilated before ever crossing the event horizon. If this is true of passenger B and his rocket ship, it is also true of the material entering the black hole that preceded him. In fact, it's true of ALL material entering the region dating back to the very instant of the black hole's formation. In my mind this implies that the black hole is never formed, the event horizon never exists. All matter brought close enough together to form a traditional black hole is essentially "frozen in time" during its journey, being released from its fate in the form of radiation.

To me this makes intuitive sense as well for the following reason: as mass approaches the Schwarzschild radius it's material can be calculated to experience a velocity approaching that of c, yet relativity forbids any non-zero mass to travel at c. Perhaps Hawking radiation is simply another way of stating the conversion of mass approaching a velocity of c into energy?

Thoughts?

*I use the term "black hole" even though what I am proposing is a "black hole region" in which a proper black hole never quite materializes, yet powerful gravitational forces exist nonetheless.

** The point of this post is that B's journey would not be uneventful. In fact, I imagine as he approached the event horizon he would experience more and more frequent collisions with more and more energetic particles which would eventually destroy him and his ship entirely before his journey was complete.

 

[zhermes]

There are lots of problems with your analysis, you should consider reading a book on the subject, for instance https://www.amazon.com/dp/0316016411/?tag=pfamazon01-20 might be well-suited for the nature of your inquest.

 

[rjbeery]

zhermes: I've read it, thanks. Basically, Susskind believes that the separate A and B frames are represented by a split, analogous to a Many Worlds Interpretation of QM. Could you be more specific about the problems with my analysis? It's a given that I am not an expert in this field but even if you do nothing but dazzle me with big words I would have something to research beyond reading another pop-sci book.

 

[George Jones]

** The point of this post is that B's journey would not be uneventful. In fact, I imagine as he approached the event horizon he would experience more and more frequent collisions with more and more energetic particles which would eventually destroy him and his ship entirely before his journey was complete.

No. According to the book Quantum Fields in Curved Space by Birrell and Davies, pages 268-269,

These consideration resolve an apparent paradox concerning the Hawking effect. The proper time for a freely-falling observer to reach the event horizon is finite, yet the free-fall time as measured at infinity is infinite. Ignoring back-reaction, the black hole will emit an infinite amount of radiation during the time that the falling observer is seen, from a distance to reach the event horizon. Hence it would appear that, in the falling frame, the observer should encounter an infinite amount of radiation in a finite time, and so be destroyed. On the other hand, the event horizon is a global construct, and has no local significance, so it is absurd to0 conclude that it acts as physical barrier to the falling observer.

The paradox is resolved when a careful distinction is made between particle number and energy density. When the observer approaches the horizon, the notion of a well-defined particle number loses its meaning at the wavelengths of interest in the Hawking radiation; the observer is 'inside' the particles. We need not, therefore, worry about the observer encountering an infinite number of particles. On the other hand, energy does have a local significance. In this case, however, although the Hawking flux does diverge as the horizon is approached, so does the static vacuum polarization, and the latter is negative. The falling observer cannot distinguish operationally between the energy flux due to oncoming Hawking radiation and that due to the fact that he is sweeping through the cloud of vacuumm polarization. The net result is to cancel the divergence on the event horizon, and yield a finite result, ..

This finite amount is negligible for observers freely falling into a black hole.

 

[rjbeery]

Thanks George.

Ignoring back-reaction, the black hole will emit an infinite amount of radiation during the time that the falling observer is seen, from a distance to reach the event horizon.

I do not understand this. Why would the author claim that the black hole would emit an infinite amount of radiation during this infinite time? The point of Hawking radiation is that the black hole dissipates slowly, essentially shrinking. The whole point of my OP was that the BH would shrink before any material were calculated to reach the event horizon. What the observer on the rocket ship would actually experience is more speculative, and really of secondary concern to me.

 

[cbstevens]

In 1982 after going through several review articles in A. Held's two volume proceedings General Relativity and Gravitation, I concluded that virtually all work on black holes and all other cosmological singularities after 1950 were the direct result of a deliberate axiomatic warfare tactic initiated by Kurt Gödel. This was in response to the terrible way in which his good friend Albert Einstein was treated by the general mathematical physicist community: They would kiss his feet, but not listen to a word he said. Basically, Gödel sent them into a theoretical black hole with a time reversal twist. After about 40 years they would climb back out, and begin all over at the same place where they began in 1950. After reading the Gödel papers and philosophical comments on relativity, this conclusion appeared obvious. This was before I came to know Stanley Tennenbaum very well, a leading collaborator of Gödel. (Note that the Princeton Library last time I checked was utilizing the well know intelligence dirty trick of listing the Tennenbaum-Gödel conversation notebooks under Tenenbaum.) From 1989 to 1993, Stanley intensively tutored me on various topics. I concluded that my original analysis was quite correct. Chuck Stevens 571-252-0451

 

[rjbeery]

That is fascinating, cb. It's very interesting to me to read the responses of Physicists, some very well educated, when I ask questions based on logic and common sense. I am not so naive as to believe that common sense is a good guide in QM and Relativity, but it should also not be thrown out the window if possible. I feel like I'm not demanding, simply questioning, whether the emperor is clothed and I am attacked and ridiculed and denounced by multiple PhDs.

If you want a chuckle check out the finale of http://www.sciforums.com/showthread.php?p=2608304#101". Do I have a point? I have no idea, I am not educated enough to make that determination. But when my questions cause such drama it makes me think that I'm not the only one with doubts.

 

[cbstevens]

Dear Friend, I have discussed this with a wide range of leading authorities and you are the first person to get the chief point: "The Emporer has no clothes!" All black holes are naked singularities. But you take it even a step further by confessing your ignorance and that you have doubts. As Socrates and Cusa demonstrate most rigorously there can be no scientific thinking without first admitting ones ignorance (Docta Ignorantia) or as Cantor might put it, one must first begin with the empty set. As Stanley Tennenbaum taught me, there are always two possibilities when one cannot understand something: 1) you are simply stupid Stevens and must try harder to understand; 2) you are right Stevens, no one can understand that, everyone who thinks he does is simply living in an illusion. Both possibilities must be thoroughly explored. And usually the second is true. The problem with most modern mathematical physicists is they are followers of Newton and Sarpi. According to them principles do not exist in our universe, and in any case should be given short shift in any scientific discussion.

 

[zhermes]

But when my questions cause such drama it makes me think that I'm not the only one with doubts.

Or at least, you shouldn't be the only one with doubts.

 

[zhermes]

All black holes are naked singularities.

Pardon?

 

[zhermes]

I concluded that virtually all work on black holes and all other cosmological singularities after 1950 were the direct result of a deliberate axiomatic warfare tactic initiated by Kurt Gödel... Basically, Gödel sent them into a theoretical black hole with a time reversal twist. After about 40 years they would climb back out, and begin all over at the same place where they began in 1950.

What?

 

[rjbeery]

Or at least, you shouldn't be the only one with doubts.

Well, if I started a thread asking whether or not lollipops were the glue that held space-time together I would not expect ad hominem attacks. When I ask a question that only generates replies attempting to establish how stupid I am, rather than address the question, it makes me think that there is a small possibility of self-doubt in the responders.

 

[cbstevens]

What I was referring to in General Relativity and Gravitation: One Hundred Years after the Birth of Albert Einstein, Vol. 2, Ed. A Held (Plenum Press, New York, 1980), was F. J. Tipler, C. J. S. Clarke and G. F. R. Ellis “Singularities and horizons: A review article” p. 97. You will find that they have an informative discussion of the collapse of the Penrose censorship theorems. Apparently our respondent is not aware of the literature on Gödel and time reversal. You can find a few articles on this here
http://scholar.google.com/scholar?q=time reversal%
20G%C3%B6del&hl=en&safe=off&um=1&ie=UTF-8&sa=N&tab=ps
Or just search in google scholar "Gödel AND time reversal." There are also an interesting range of books on the topic.
Well my friend with respect to ad hominem, I think you will find that underneath their skin these mathematical physicists act more like berserkers when properly nailed down. Or to put more cordially, they simply refuse to discuss the scientific record.

 

[bcrowell]

It seems to me that the OP's question is basically the question that Susskind's idea of black hole complementarity was meant to answer. There is already a sizable literature on black hole complementarity, and it's clearly highly controversial. If you do a little googling, you can find respected relativists saying that the idea is wrong, and others saying that the idea is right. Those who say it's wrong basically seem to think that the paradox it was meant to resolve is in fact a non-paradox. I doubt that we're going to resolve the controversy here. If someone has a favorite review article on this topic that's on arxiv, we could read it.

 

[bcrowell]

Cbstevens, rjbeery's question was about Hawking radiation, an idea that dates back to the mid-70's. I, like zhermes, don't understand what you meant by #6, but the dates seem to indicate that it can't have anything to do with Hawking radiation. If you would like to start a separate thread about your take on the classical issues involving black holes, that might be interesting, but this thread is about a quantum-mechanical topic.

 

[cbstevens]

We could begin by discussing Lawrence B. Crowell, "Generalized Heisenberg Uncertainty Principle for Quantum Fields in Curved Spacetime," Foundations of Physics Letters, 12(6), Dec. 1999, p. 585-591. If you have a copy please forward it to chuckstvns@gmail.com. And possibly this: Quantization effects in the plasma universe
Wells, Daniel R.; Bourouis, Mohammad
AA(Miami, University, Coral Gables,
FL), AB(Miami, University, Coral Gables, FL)
Publication: IEEE Transactions on Plasma Science
(ISSN 0093-3813), vol. 17, April 1989, p. 270-281.
04/1989
Abstract
It is suggested that a unification of the morphology of the solar system, anomalous intrinsic red shifts of
quasars and galaxies, the structure of the hydrogen atom, the Einstein equations of general relativity,
and Maxwell's equations can be accomplished by a basic consideration of the minimum-action states of
cosmic and/or virtual vacuum-field plasmas. A formalism of planetary-formation theory is
generalized to describe relativistic gravitational field theory in terms of a pregeometry. A virtual plasma
associated with the vacuum state is postulated. It is demonstrated that the relaxed state of the virtual
plasma underlies Einstein's field equation and predicts (1) the effective gravitational potential
generated by the Schwarzschild solution and (2) the structure of the hydrogen atom described in terms of
the Schroedinger equation of quantum mechanics. These concepts are applied to explain the quantized
anomalous red shifts in related galaxies observed by Arp and Sulentic (1985).

 

[rjbeery]

http://www.newscientist.com/article/dn12089-do-black-holes-really-exist.html" was pointed out to me on another forum, which I was relieved to see if only for the reason that there is at least one Physicist who was wondering the same thing I was.

I've read Susskind's book on Blackholes, and I have to respectfully disagree with his take. I am certainly less qualified on paper than Dr. Susskind on the matter, but that alone cannot stifle all curiosity. I prefer a Real, Local interpretation of the Universe which does not allow for dichotomies of experience (or multiple worlds, etc). I don't mean to morph this into a discussion on QM interpretations, but the subject is unavoidable if we talk about Susskind.

 

[cbstevens]

My dear friend rjbeery, I must leave you now. I have found what I was looking for, without looking. Keep up the good work of your questions. If you suffer any future PhD ad homenining, please contact me chuckstvns@gmail.com.

 

[chronon]

I've read Susskind's book on Blackholes, and I have to respectfully disagree with his take.

I think you're misunderstanding what Susskind is saying. It isn't that there's a many worlds type split, in which one person falls into the singularity while another gets spread out over the event horizon. Rather, according to the outside world the infaller is spread out over the horizon, but the infaller experiences this as crossing the horizon towards the singularity. This isn't so very different from two observers finding different lengths for the same object in special relativity. (Not that I necessarily believe it - I'm very suspicious of anything involving Complementarity)

 

[rjbeery]

Well, if I were to speak purely as a speculating layman, is it possible that the Hawking radiation (or even simply the CBR) could act as a destructive force as the mass of an infalling observer were subjected to near-infinite accelerative forces near the EH? This would resolve the dichotomy, as both local and infinite frames would see the infalling mass destroyed before the EH was reached.

*edit* Rereading your post, you are saying that Susskind is claiming that there is no dichotomy at all, and that maybe the infaller continues to remain physically viable, even if the infinite frame calculates that his matter has been scattered to all corners of the EH. Very interesting, but it still doesn't really resolve the common sense objections I have.

 

[Chronos]

An issue to consider is whether a true 'singularity' can form in our spacetime. There is little doubt an event horizon can form.

 

[rjbeery]

There is little doubt an event horizon can form

I agree about the singularity, but I also question the EH itself. Maybe you can help me find the problem with my logic.

1. Do you agree that all frames outside of the BH calculate that no mass ever crosses the EH (or, more specifically, mass crosses the EH at t=infinity)?

2. Do you agree that the EH does not expand until mass has crossed the EH (i.e. backreaction)?

If you concur with #1 and #2, then run the clock backwards in your mind and describe to me how this theoretical black hole formed in the first place. There are other problems that I have as well, but let's start here...

 

[bcrowell]

An issue to consider is whether a true 'singularity' can form in our spacetime.

This has been settled for a long time, in GR, and the answer is yes: http://en.wikipedia.org/wiki/Penrose–Hawking_singularity_theorems

 

[zhermes]

I agree about the singularity, but I also question the EH itself. Maybe you can help me find the problem with my logic.
1. Do you agree that all frames outside of the BH calculate that no mass ever crosses the EH (or, more specifically, mass crosses the EH at t=infinity)?
2. Do you agree that the EH does not expand until mass has crossed the EH (i.e. backreaction)?
If you concur with #1 and #2, then run the clock backwards in your mind and describe to me how this theoretical black hole formed in the first place. There are other problems that I have as well, but let's start here...

Before you "question" the validity of a theory, you should try to learn it. If nothing else your use of language (e.g. "more specifically, mass crosses the EH at t=infinity") suggests you don't have a good handle on mathematics, nor general relativity. To dissuade your current qualms, see: http://www.mathpages.com/rr/s7-02/7-02.htm
For a longer-term study, see Hartle's "Gravity: An Introduction to Einstein's General Relativity," for instance.

 

[Chronos]

This has been settled for a long time, in GR, and the answer is yes: http://en.wikipedia.org/wiki/Penrose–Hawking_singularity_theorems

From the referenced Wiki article:
" ... It is still an open question whether time-like singularities ever occur in the interior of real charged or rotating black holes ..."
And
" ... Hawking's singularity theorem is for the whole universe, and works backwards-in-time: in Hawking's original formulation, it guaranteed that the Big Bang has infinite density. Hawking later revised his position in "A Brief History of Time" (1988) where he stated "There was in fact no singularity at the beginning of the universe" (p50). This revision followed from quantum mechanics, in which general relativity must break down at times less than the Planck time. Hence general relativity cannot be used to show a singularity."

 

[JustinLevy]

I agree about the singularity, but I also question the EH itself. Maybe you can help me find the problem with my logic.

1. Do you agree that all frames outside of the BH calculate that no mass ever crosses the EH (or, more specifically, mass crosses the EH at t=infinity)?

2. Do you agree that the EH does not expand until mass has crossed the EH (i.e. backreaction)?

If you concur with #1 and #2, then run the clock backwards in your mind and describe to me how this theoretical black hole formed in the first place. There are other problems that I have as well, but let's start here...

I think this discussion will take way too long if we approach it from this route. I suggest simplifying this as greatly as possible to get at the heart of the confusion here. We can discuss the underlying confusion without even needing GR. Quantum mechanics in flat spacetime + SR is enough.

Consider a Rindler horizon, and the associated Unruh radiation.

Just like in your openning paragraph, an observer far from the horizon and thus experiencing negligible proper acceleration (you could go to infinity to get your "infinity" observer as you call him) will see a object approaching the horizon take infinite time according to his watch to reach the horizon. He will also see the object bathed by an infinite amount of radiation before reaching the horizon.

Let's consider this scenario: described from an inertial frame, we see the global structure that is the rindler observer's event horizon. Imagine a baseball made of normal matter, and a baseball made of anti-matter. The baseball is on one side of the event horizon (inside the Rindler observer's past light cone), and the anti-baseball is on the other side. The baseball is thrown towards the horizon, and the antibaseball is in a trajectory so it is on the otherside to meet the baseball just as it crosses.

Alright, this is just good old flat-spacetime. What happens?

If the Rindler observer is always at constant acceleration, the baseball with never reach the horizon in any finite time on his watch. The baseball will be bathed with infinite amount of radiation.

From the baseball point of view, nothing spectacular happens as it crosses the horizon, and it reaches it in finite proper time. Upon crossing the horizon, it is annihilated, but the radiation from that anhihilation can never reach the Rindler observer.

Yes, to our intuition these sound contradictory.
But no, the math is consistent. Where our intuition fails is the expectation of "observer independence" of particle number.

Do we at least agree to this point?

The next issue of intuition failure is the fact that the Rindler observer's coordinate chart doesn't cover all of spacetime. So while what you are implying would be like claiming the "annihilation event" never occurred according to the Rindler observer, that is not actually the case. He doesn't have a coordinate to assign to that event, according to his coordinate chart. That is completely separate from the claim that the event doesn't occur. He also cannot physically measure that it occurs, since the event is outside his light cone, but again, that is distinct from claiming the event didn't occur. For the event did, objectively occur.

So the second intuition issue is taking coordinate labels as too "physical". I have trouble describing this one well (it's come up in many other contexts with people asking questions on this site, and I'm often not able to help them see this clearly). So hopefully someone can word or describe it much better than I. Anyone? Please? I would like to learn how to describe this better.

 

[JustinLevy]

This has been settled for a long time, in GR, and the answer is yes: http://en.wikipedia.org/wiki/Penrose...arity_theorems

From the referenced Wiki article:
" ... It is still an open question whether time-like singularities ever occur in the interior of real charged or rotating black holes ..."
And
" ... Hawking's singularity theorem is for the whole universe, and works backwards-in-time: in Hawking's original formulation, it guaranteed that the Big Bang has infinite density. Hawking later revised his position in "A Brief History of Time" (1988) where he stated "There was in fact no singularity at the beginning of the universe" (p50). This revision followed from quantum mechanics, in which general relativity must break down at times less than the Planck time. Hence general relativity cannot be used to show a singularity."

You may be missing the point here.
bcrowell is correct. This has been settled for a long time, in GR, and the answer is yes.
There is no question whether, according to GR, time-like singularities form in the interior of black holes formed from the infall of realistic starting conditions of stellar matter (ie. it isn't an artifact of very specific initial conditions).

The issue is instead, the real world clearly isn't completely classical as we have quantum mechanics. So in the real world, does a singularity form? Hawking isn't contradicting or revising, he is clarifying that his theorem was for GR and what happens in Quantum-Gravity is still not settled since we don't have a theory of quantum gravity that we can run the predictions with yet.

Maybe you already agree with all that, and we're on the same page. I just wanted to make sure.

That being said, most people wouldn't consider a theory of quantum-gravity that predicted singularities as being a consistent theory. GR's applicable domain does not cover short length scales as it is a classical theory, but quantum-gravity would have no excuse. Finding a theory predicts that it can't even predict further evolution (due to singularity), would make it not consistent and predictive. For this reason, there really isn't even debate amongst people looking for a theory of quantum-gravity whether there are black hole singularities "in the real world". They believe there exists a consistent theory of quantum-gravity (even if it hasn't been completely worked out / found yet), which without even getting details can make the prediction (just due to being predictive and consistent) as: no.

So there really isn't much debate on either side.

 

[DavidGTaylor]

If there isn't debate, there needs to be. The border of a Black Hole/Schwarzschild object is not a wall, it is a marker where actual 'escape' requires light velocity. There is no reason why an object moving at orbital velocity for that S.O. would not simply pass the border and go into orbit. You maybe could make proclamations about relativistic distortion slowing things down so that normal physics doesn't apply, but think about this.
If our Universe has a mass (just a proposition) of 1.0E+53 kg, then the radius of an S.O with that mass would be about 1.535E+26m or 1.623E+10 light years. The gravity at that point would be 2.93E-10 m/s^2. Current theory says that distortion is infinite at that point?

 

[JesseM]

If there isn't debate, there needs to be. The border of a Black Hole/Schwarzschild object is not a wall, it is a marker where actual 'escape' requires light velocity. There is no reason why an object moving at orbital velocity for that S.O. would not simply pass the border and go into orbit.

What does S.O. stand for? Anyway, there is no "orbital velocity" at distances closer than the photon sphere, which is at a radius of 1.5 times the radius of the event horizon (i.e. there is a region between the photon sphere and the event horizon where it is possible to escape for an object traveling outward in the radial direction with sufficient speed, but it is impossible for anything to be in a circular orbit no matter how fast its speed in the nonradial direction) And once you are at or inside the "border" that is the event horizon, it's impossible for anything to escape (except for a hypothetical particle moving faster than light, but it's generally assumed these don't exist)

 

[rjbeery]

zhermes, thanks for the link. I read it all yet I still have problems.

We saw that the radial position of a test particle starting at radius r = 10m and t = 0 (for example) as a function of the particle’s proper time is a simple cycloid right down to r = 0, whereas if the same trajectory is described in terms of Schwarzschild coordinate time, the infalling object traverses through infinite coordinate time in order to reach the event horizon, and then traverses back through an infinite range of coordinate times until reaching r = 0 (in the interior) in a net coordinate time that is not too different from the elapsed proper time. In other words, the object goes infinitely far into the "future" (of coordinate time), and then infinitely far back to the "present" (also in coordinate time), and since these two segments must always occur together, we can "re-normalize" the round trip and just deal with the net change in coordinate time (for any radius other than precisely r = 2m).

I am not challenging the mathematical model of GR; I am applying common sense to what we can consider to be the real-world model of black holes. Be honest, does the above maneuver sit well with you? Claiming, basically, that infinity minus infinity gets us back to a finite proper time? It doesn't really matter because the author goes on to say

the "frozen star" interpretation does have the advantage of simplifying the topology, i.e., it allows us to exclude event horizons separating transfinite regions of spacetime. More importantly, by declining to consider the fate of infalling worldlines through the event horizon, we avoid dealing with the rather awkward issue of a genuine spacetime singularity at r = 0. Therefore, if the "frozen star" interpretation gave equivalent predictions for all externally observable phenomena, and was logically consistent, it would probably be the preferred view. The question is, does the concept of a "frozen star" satisfy those two conditions? We saw above that the idea of a frozen star as an empty region around which matter "bunches up" outside an event horizon isn't viable, because if nothing ever passes from the exterior to the interior of an event horizon (in finite coordinate time) we cannot accommodate infalling matter. Either the event horizon expands or it doesn't, and in either case we arrive at a contradiction unless the value of m inside the horizon increases, and does so in finite coordinate time.

I guess I don't know the strict definition of a "frozen star", but my "black hole region" contains no event horizon. It appears that the author, as I did, questions the process of growth of the event horizon, however his PRESUMPTION of the EH's existence forces him to reject the frozen star rather than rejecting the EH itself. Note that the author claims that, but for this "logical inconsistency", the frozen star would be the preferred view, and I am claiming that the inconsistency does not exist.

Furthermore, the author relies on the experience of the infalling frame as "evidence" that the frame is viable. Although admittedly speculative, I have suggested that the infalling masses are destroyed through the pre-Hawking radiation process.

 

[JesseM]

I am not challenging the mathematical model of GR; I am applying common sense to what we can consider to be the real-world model of black holes. Be honest, does the above maneuver sit well with you? Claiming, basically, that infinity minus infinity gets us back to a finite proper time?

But that's just in a particular coordinate system which is badly-behaved on the horizon, namely Schwarzschild coordinates. Other coordinate systems on the same spacetime don't say the coordinate time to reach the horizon is infinite--see Kruskal-Szekeres coordinates for example. And contrariwise, even in ordinary boring flat SR spacetime you can come up with coordinate systems that are badly-behaved at some boundary, in the sense that the coordinate time to cross that boundary is infinite--this is true of Rindler coordinates, an accelerating coordinate system in flat spacetime where it takes an infinite coordinate time for anything to cross the Rindler horizon (in fact there is a close analogy between these cases, if you plot lines of constant Rindler position and Rindler time in an ordinary Minkowski diagram where the vertical and horizontal axes are those of an inertial frame, it looks just like what you get if you plot lines of constant Schwarzschild position and Schwarzschild time in a diagram where the vertical and horizontal axes are those of Kruskal-Szkeres coordinates...compare the yellow diagram on the Kruksal-Szkeres wikipedia page with the second diagram on the Rindler horizon page).

Basically the lesson is, don't take "coordinate singularities", where some coordinate-based quantity like the time dilation of a clock relative to coordinate time goes to infinity, too seriously. The only singularities that are really physical are ones where some coordinate-invariant quantity goes to infinity, like singularities in the curvature of spacetime which occur at the center of a black hole. Likewise the only notion of "time" that's really physical is proper time along some worldline, and both Schwarzschild coordinates and Kruskal-Szekeres coordinates predict it only takes a finite proper time for an infalling observer to cross the horizon (though in terms of Schwarzschild coordinates, what you'd actually show is that in the limit as the distance between the falling observer and the horizon goes to zero as the coordinate time goes to infinity, the proper time approaches a particular finite value, the exact same value that in Kruskal-Szekeres coordinates is the proper time of the falling observer at the moment she crosses the horizon).

 

[rjbeery]

I respectfully disagree. Kruskal coordinates have problems with the OP also (remember, I am using the infinite observer's frame which presents Kruskal indeterminability). My OP is quite simple: if the black hole region evaporates in finite time, and mass crosses the EH in "infinite" time, then then black hole region is gone before any mass reaches it. It really doesn't need to be much more complicated than that, and the aesthetic advantages of this interpretation are indisputable (aren't they?).

 

[JesseM]

I respectfully disagree. Kruskal coordinates have problems with the OP also (remember, I am using the infinite observer's frame which presents Kruskal indeterminability).

What does "Kruskal indeterminability" mean? What exactly is indeterminable? Remember that Susskind's discussion of two different opinions on what happens to the falling observer had to do with speculations about quantum gravity, there are no such disagreements in classical general relativity (although certain observers may not be able to see certain events that others can see due to event horizons)

Also, note that observers don't really have "frames" in general relativity, except for locally inertial frames in regions of spacetime small enough that the curvature is insignificant. In SR we can talk about an observer's frame as just a shorthand for the inertial frame where they are at rest, since there is a unique way to construct an inertial frame for any inertial observer (aside from the position of the origin and the orientation of the spatial axes), and inertial frames are "preferred" in SR (the basic equations of SR like time dilation only hold in inertial frames, and the laws of physics obey the same equations in all inertial frames). But in GR the principle of "diffeomorphism invariance" means that the equations of GR hold in any arbitrary coordinate system, so there are an infinite number of different ways you could construct a coordinate system where a given observer in curved spacetime is at rest, and none of these different coordinate systems would be preferred over any other. So, talking about an observer's "frame" in a decent-sized region of curved spacetime does not pick out any unique coordinate system, and thus the term isn't really meaningful in this context, so physicists don't talk about the "frames" of GR observers.

My OP is quite simple: if the black hole region evaporates in finite time, and mass crosses the EH in "infinite" time, then then black hole region is gone before any mass reaches it.

What does "mass crosses the EH in infinite time" mean, though? Are you talking about coordinate time in some coordinate system, and if so which one? If the black hole evaporates in finite time, I don't think you can use Schwarzschild coordinates which are specific to the Schwarzschild spacetime which describes an eternal black hole. And even in this spacetime you can find coordinate systems (like Kruskal-Szkeres) where mass crosses the EH in a finite coordinate time.

Perhaps you're not talking about coordinate time at all, but rather what is seen visually by some observer outside the horizon (i.e. the proper time according to their own clock when they receive various light signals from events on the worldline of an object falling in). In the case of an eternal Schwarzschild black hole, it is true that if a falling clock is ticking as it falls in, the proper time for an external observer between seeing the light from successive ticks will get larger and larger, and the outside observer will never get to see the clock reading the exact time it read at the moment it crossed the horizon. However, for an evaporating black hole the situation is probably different, in theory the outside observer would see the light from the falling observer cross the horizon at the exact moment the outside observer sees the black hole evaporate to nothing (with the understanding that this theoretical answer would only hold if light waves were emitted continuously by the falling observer rather than in discrete photons, and if the outside observer could still see light at extremely high finite redshifts), as discussed in the last section of this entry from the Usenet Physics FAQ:

What about Hawking radiation? Won't the black hole evaporate before you get there?

(First, a caveat: Not a lot is really understood about evaporating black holes. The following is largely deduced from information in Wald's GR text, but what really happens-- especially when the black hole gets very small-- is unclear. So take the following with a grain of salt.)

Short answer: No, it won't. This demands some elaboration.

From thermodynamic arguments Stephen Hawking realized that a black hole should have a nonzero temperature, and ought therefore to emit blackbody radiation. He eventually figured out a quantum- mechanical mechanism for this. Suffice it to say that black holes should very, very slowly lose mass through radiation, a loss which accelerates as the hole gets smaller and eventually evaporates completely in a burst of radiation. This happens in a finite time according to an outside observer.

But I just said that an outside observer would never observe an object actually entering the horizon! If I jump in, will you see the black hole evaporate out from under me, leaving me intact but marooned in the very distant future from gravitational time dilation?

You won't, and the reason is that the discussion above only applies to a black hole that is not shrinking to nil from evaporation. Remember that the apparent slowing of my fall is due to the paths of outgoing light rays near the event horizon. If the black hole does evaporate, the delay in escaping light caused by proximity to the event horizon can only last as long as the event horizon does! Consider your external view of me as I fall in.

If the black hole is eternal, events happening to me (by my watch) closer and closer to the time I fall through happen divergingly later according to you (supposing that your vision is somehow not limited by the discreteness of photons, or the redshift).

If the black hole is mortal, you'll instead see those events happen closer and closer to the time the black hole evaporates. Extrapolating, you would calculate my time of passage through the event horizon as the exact moment the hole disappears! (Of course, even if you could see me, the image would be drowned out by all the radiation from the evaporating hole.) I won't experience that cataclysm myself, though; I'll be through the horizon, leaving only my light behind. As far as I'm concerned, my grisly fate is unaffected by the evaporation.

All of this assumes you can see me at all, of course. In practice the time of the last photon would have long been past. Besides, there's the brilliant background of Hawking radiation to see through as the hole shrinks to nothing.

(Due to considerations I won't go into here, some physicists think that the black hole won't disappear completely, that a remnant hole will be left behind. Current physics can't really decide the question, any more than it can decide what really happens at the singularity. If someone ever figures out quantum gravity, maybe that will provide an answer.)

 

[DavidGTaylor]

Lets get one thing straight. Velocity is not the exclusive element in escape velocity. There aren't Classic Gravitational theory speed traps at the border stopping object if it isn't going fast enough. The whole reason escape/orbital velocity works is because the momentum acquired by the escaping body allows it to coast completely out of the body's gravitational influence. But in a relativistic world a 1 kilo object does not need velocity of 299,792,458 m/s to escape. It needs a momentum of: 299,792,458 kg*m/sf. And if you were paying attention when Dr. Einstein was spouting that "Relativity" mass increase business in class last century, you would be able to calculate that a body with a rest mass of 1 Kg has momentum of 299,792,458 kg*m/s when it is going a little more than 2.11985E+08 m/s.

 

[JesseM]

Lets get one thing straight. Velocity is not the exclusive element in escape velocity. There aren't Classic Gravitational theory speed traps at the border stopping object if it isn't going fast enough. The whole reason escape/orbital velocity works is because the momentum acquired by the escaping body allows it to coast completely out of the body's gravitational influence.

The event horizon is not simply the distance where the "escape velocity" is the speed of light. "Escape velocity" is a concept from Newtonian physics which does not really explain what's going on in general relativity, although authors writing for a popular audience do sometimes simplify the concept of an event horizon in this way. In Newtonian physics, it's quite true that if the escape velocity at radius R is v_R, an object traveling outward from just under R with v < v_R can travel out past R, it just won't "escape" in the sense that it will eventually start falling back down. However in GR, where we are dealing with curved spacetime, the situation is totally different--for any event which occurs on or inside the event horizon, spacetime is curved in such a way that the entire future light cone of that event remains inside the horizon, so no worldlines passing through that event can even briefly stray outside the horizon. This can be illustrated nicely if we use Eddington-Finkelstein coordinates, where the future light cones of different events actually tilt over for events closer to the horizon (as discussed here), you can see visually that future light cones of events on or inside the horizon don't have any part outside the horizon:

[URL]http://www.etsu.edu/physics/plntrm/relat/eventho1.gif[/URL]

[URL]http://www.etsu.edu/physics/plntrm/relat/eventho2.gif[/URL]

(images from http://www.etsu.edu/physics/plntrm/relat/blackhl.htm)

But in a relativistic world a 1 kilo object does not need velocity of 299,792,458 m/s to escape. It needs a momentum of: 299,792,458 kg*m/sf.

Again, you appear to be thinking in terms of classical escape velocity, but the event horizon cannot be understood in this way. Also, in relativity momentum is not given by (rest mass)*(velocity), it is given by (rest mass)*(velocity)*gamma, where gamma is the relativistic factor $$\frac{1}{\sqrt{1 - (v/c)^2}$$. So, in the limit as v approaches c, gamma (and thus the momentum of any object with nonzero rest mass) approaches infinity.