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What's inside a black hole?

  1. Nov 17, 2006 #1
    I've been reading about relativity for several years, but I'm no physicist or mathematician. This question has been bothering me lately, and I'm hoping someone out there can help me understand. I don't have the math to express this briefly, so here it is in words...

    When a particle of matter crosses the event horizon of a black hole, what is its velocity with respect to the outside? Intuitively, I think that the velocity approaches the speed of light, c, as the particle approaches the horizon. At the point that it would hypothetically cross the horizon, I think that the particle would have the velocity c.

    In my mental image of what is happening, I see the particle accelerating as it approaches the horizon. Time dilation makes the particle age more and more slowly relative to the rest of the universe, approaching zero as the particle approaches the horizon.

    So, in the proper time of the particle, when it crosses the horizon, what time is it outside of the black hole? I think that the answer must be that an infinite time has passed there. The end of time has come and gone. The universe has ended. There is no universe any more.

    If that is true, then why would we expect anything to be "inside" a black hole? There has not been enough time since the beginning of the universe for anything to have crossed an event horizon. From the perspective of the outside universe, the inside of a black hole does not exist, and will never exist as long as the universe outside still exists.

    I understand that the inside exists for the particle, and that you can follow the particle across the horizon, using the appropriate coordinate system, and that nothing special happens at the horizon. From the particle’s perspective, the space-time inside the black hole (up to the singularity) seems to be a smooth continuation of the space-time outside of the black hole. That does not mean that it exists during the lifetime of the outside universe.

    From this point of view, the “contents” of the black hole are essentially a two-dimensional boundary that surrounds a hole in the universe. The black hole, its event horizon and its central singularity don’t exist. The universe ends at the point just outside of the horizon, which is reached by the in-falling particle only after an infinite (outside) time.

    For this to be true, the space near the horizon must be fantastically curved. There has to be enough space there for a particle to travel “forever” at almost the speed of light. How can that be reconciled with the low tidal forces that I’ve heard are found at the event horizons of large black holes? I guess that the answer is that the space is not “curved”, but “radially distorted”. Length contraction of the in-falling particle (from the outside view) does not fully explain this. The in-falling particle would still cover the short distance at the speed of light. It must be that space itself is radially stretched at the event horizon, to allow an infinite time for the particle to reach the horizon.

    So is there anything inside a black hole? If so, where have I gone wrong? If not, why do we talk about black holes as if they were objects with an inside? I wonder if there is any essential difference between the end of the universe at the event horizon, and the “plain old” end of the universe everywhere else.

    Wondering...Jim
     
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  3. Nov 17, 2006 #2
    since the escape velocity for a black hole exceeds c when you are inside the event horizon I would expect that objects falling towards the black hole horizon will have speeds that approach c.

    its probably a bad analogy, but:

    if you throw something upwards it reaches a point when it is at rest, then afterwards behaves as if it was falling from rest to the ground.

    when it reaches the ground it has the same velocity as when it was launched, but in the opposite direction.

    now, with a black hole we can do the same, the nearer we get to the event horizon the nearer to c we must launch our object at... so when it falls back down it should also be falling at a speed near to c...

    As for what is inside the hole though? That is why we call it black. We can't see inside it or through it. :p
     
  4. Nov 17, 2006 #3
    It's nothing. Everything what the black hole is, is the event horizon. Quantum screen, everything is going on there.
     
  5. Nov 17, 2006 #4

    pervect

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    We've had another recent thread on the same topic.

    You need to remember that simultaneity is relative. So the answer of "what age is the universe when the particle crosses the event horizon" does not have an absolute answer.

    What you should focus on is when light signals arrive, and when they are received. If an infalling observer watches a distant beam of light, he will observe modest and finite redshifts or blueshifts, depending on his exact trajectory. If the infalling observer free-falls from infinity, he sees the incoming light redshifted to half its original frequency at the event horizon.

    Thus the infalling observer does not see the whole history of the universe play out before him.

    See also http://www.math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html

    which was also mentioned (several times) in the last thread.

     
  6. Nov 18, 2006 #5
    This is a quote from that Baez article:
    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).​
    So, if the outside observer never sees anything encounter the event horizon, then from that frame of reference, nothing ever makes it inside during the lifetime of the universe. For an eternal black hole, nothing ever leaves our universe during its lifetime. So nothing is ever “inside” the black hole. The next paragraph in the Baez article says:

    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.​

    So the question of what is inside a black hole applies only to “mortal” black holes. On the other hand, the “mortal” black hole ceases to exist when the in-falling particle reaches the horizon, so nothing is ever “inside” in that case, either. The particle does, however, reach the horizon in a finite (outside) time.

    This is where I was headed – if nothing is inside, hidden by the horizon, then why are we concerned about an information paradox. Now I see that the in-falling object can disappear from the universe in finite time, and the information paradox will require some more thought on my part…Jim
     
  7. Nov 19, 2006 #6

    Chris Hillman

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    Velocity of particle inside even horizon, measured by observer outside?

    Hi, Jim,

    You have certainly raised many issues here!

    Unfortunately, you appear to have rather badly misunderstood what Baez was trying to tell you. He certainly was NOT saying that only "eternal" holes have an interior--- in fact, the whole point was to explain why one should think of "mortal" holes pretty much like one thinks of the eternal ones (the kind modeled by gtr; the "mortality" he refers to requires additional ideas from quantum field theory). I don't want to even try to explain the points which are confusing you (it should help to remark that these points confuse just about everyone when they first encounter gtr), but I DO have a constructive suggestion for you.

    You hinted that you don't have a strong mathematical background. In general that is a huge handicap, but fortunately, if you have a strong visual imagination, I believe that you should be able to come to a correct understanding of infall into a black hole, without learning ANY mathematics, from the excellent popular book by Robert Geroch, General Relativity from A to B. Geroch is a leading expert on gtr and he devotes the book to a very careful pictorial exposition which clears up the most common misunderstandings in a very clear but entirely nontechnical manner (as I recall, there is only one equation offered in the entire book--- the pictures will tell you what you need to know.)

    I also have some comments which will go way over your head, but you might make a mental note and ask a followup after you've had a chance to study Geroch, re-read Baez, and so on. These comments may also interest other readers here who may have the background to appreciate them immediately.

    The question of what the interior of realistic black hole models in gtr is like is one of current interest in classical gravitation. It is important to note that the "no hair" theorems say in effect that the EXTERIOR of black holes all "look more or lesss alike" (Kerr geometry) once they have radiated away any imperfections, but this does not apply to the INTERIOR, where a key issue (pointed out by Penrose) is that INSIDE the horizon, by definition, perturbations, e.g. from infalling and matter and radiation, certainly cannot be "radiated off to infinity" and indeed they can in a sense "collect" along a Cauchy horizon (say in the interior Kerr geometry). One important development here was the advent of the Poisson-Israel model. Another was the discovery by Chandrasekhar and his students of a beautiful "duality" between models of black hole interiors and models of the "interaction zones" of certain colliding plane wave (CPW) models in gtr. Indeed, it turns out that according to gtr, in principle you can create in some region a geometry which is locally isometric to part of the interior (think roughly of the region m < r < 2m) of a black hole by making two carefully crafted gravitational waves (one or both may be accompanied by EM or other radiation) collide! The adjective LOCALLY is essential here.

    Jheriko: you wrote "I would expect that objects falling towards the black hole horizon will have speeds that approach c". This is quite wrong; clearing up your confusion involves explaining some of the same issues about velocities in curved spacetimes which I discussed in another thread earlier today. You added "As for what is inside the hole though? That is why we call it black. We can't see inside it". This raises an interesting and important point: according to gtr, observers can certainly fall into a black hole and make physical measurements there, they cannot report their results back to their colleagues outside! This certainly poses an interesting challenge for the standard viewpoint of the relationship between theory and experiment in physics, although so far, this is only a theoretical philosophical issue, as it were!

    Tomaz: I hope you were being facetious, but few if any physicists would agree with your claim. You might be thinking of the "holographic principle", but if so I think you seriously misrepresented that idea (which again goes outside gtr for inspiration; it is helpful to try to always set a theoretical context for discussion in order to avoid confusion).

    Chris Hillman
     
  8. Nov 19, 2006 #7
  9. Nov 19, 2006 #8

    George Jones

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    Actually, I think it makes sense to interpret JHeriko's post in terms of speeds with respect to (a sequence of) observers that "hover" with constant r, theta, and phi.
     
  10. Nov 19, 2006 #9

    Chris Hillman

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    A valid interpretation

    Hi, George,

    Hmm... OK, I see what you mean, and I agree. But I think his post shows why this line of thinking can be misleading!

    Chris Hillman
     
  11. Nov 28, 2006 #10
    Thanks for the recommendation, Chris Hillman. I’ve ordered the Geroch book. I just bought “Gravitation” by Misner, Thorne and Wheeler, but it looks like it will take me a long time to get to the answers there.

    I understand and believe that a black hole has an interior, from the perspective of someone inside the horizon. My question was posed from the perspective of someone OUTSIDE the horizon. When does the outside observer witness anything being hidden by the horizon?

    Perhaps the math would help me. I don’t expect a particle to reach the horizon at all, since the space ahead of the particle is stretched as much as the space behind (probably more). But maybe that is my problem? I’ve been thinking of the particle as accelerating, therefore limited to speeds less than c relative to the outside observer. Since the horizon is receding at c from the outside perspective, I expected the outside observer to never witness the encounter of the particle with the horizon within a finite time. Does stretching space somehow allow the outside observer to see particle speeds exceeding c?

    So how long does it take (from the outside observer’s perspective) for a particle to reach the horizon? Starting with solar-system-scale distances and speeds, and having the observer accelerate to remain outside the horizon forever; can someone tell me how to calculate the time?

    Thanks...Jim
     
  12. Nov 28, 2006 #11

    Chris Hillman

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    Another Schwarzschild vacuum thought experiment

    Excellent! I'd encourage you to look at all the pictures in MTW but don't expect to understand very much until Geroch arrives. I think you'll really like both books once you get into them. (Don't worry, Geroch is MUCH shorter and less demanding, but it has really good pictures.)

    Either MTW math plus pictures or Geroch pictures should disabuse you of this expection. (I assume you are asking about what is the prediction of gtr, a somewhat different question from the issue of whether or not this prediction is fulfilled in nature.)

    Gosh, I think I see quite a few common misconceptions here. Fortunately, Geroch and MTW should be just what you need to become accustomed to the many ways in which your Newtonian and flat space intuition needs to adapt in order to give you an adequate intuitive understanding of spacetime and curvature.

    Since I just wrote a lengthy post pointing out the existence of multiple competing notions of "distance" in the Schwarschild geometry, I'll just add that above when you refer to "speed" you are probably tacitly assuming that speeds measured over noninfinitesimal distances have a unique meaning, if we fix an observer and a target. But this isn't true, because noninfinitesimal "distances" do not have a unique meaning,
    even if we fix an observer and a target.

    Good grief, Jim, we must be on the same wavelength because you just asked the very question I studied in the very next page of my voluminous notes which I was referring to while writing the post I just mentioned. I'll have to leave that until tommorrow, but the post on distances should keep you happily occupied tonight, though.
     
    Last edited: Nov 28, 2006
  13. Nov 28, 2006 #12
    I wasn't considering any particular observer, just that as an object is "launched" and then falls there is a certain symmetry. If the object is launched with some velocity v normal to a sphere creating a spherically symmetric field and then returns to the same point (whilst on its freely falling trajectory) then the 'energy gained' by 'climbing the potential', which is converted from kinetic energy to reach the top, is converted back on the way down. Assuming no losses the velocity should be the same... which ever observer you decide to be this should hold true, even if something else appears to happen because of all the curvature. Correct? Or am I missing something?

    Maybe my idea is "too classical" for discussion of a black hole...
     
  14. Nov 29, 2006 #13

    Chris Hillman

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    Hi, Jheriko, can you clarify the question? Since there has been some confusion over what thought experiment you have in mind, perhaps you can restate this as clearly as possible?

    Chris Hillman
     
  15. Dec 2, 2006 #14
    Yes, that is what I am thinking about "speed". Is that not true in GTR?

    I got tired of slogging through MTW from the beginning, so I skipped ahead, looking at the pictures as you suggested. I think I did find something relevant to my question in Firgure 25.5, page 667 of my copy. It shows a diagram of r/M versus time/M for a particle falling into a black hole, as seen by both a “co-moving observer” labeled “Proper time” and a “faraway observer” labeled “Schwarzchild time”.

    The caption says in part “In the one description [co-moving observer], the point r=0 is attained, and quickly. In the other description, r=0 is never reached and even r=2M is attained only asymptotically.” I take this to mean that the “faraway observer” never sees the particle cross the event horizon, so he should never worry that it is hidden by the event horizon. That is what I am trying to understand about the information paradox.

    The Baez article did help me see that an evaporating black hole can be a problem in this regard – it disappears in finite time, so I can understand why there might be concern about the information content of the detritus versus the original in-falling objects. I now seem to recall something to this effect in my earlier reading. I guess that maybe I don’t understand what the information paradox is about (just one of the many things that I don’t understand).

    I appreciate your patience with me, and I look forward to your future posts on this and other threads. Thanks...Jim
     
  16. Dec 2, 2006 #15

    Chris Hillman

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    Where oh where is that post where I...?

    Hi, Jim,

    I wrote "Since I just wrote a...
    ...pointing out the existence of multiple competing notions of "distance" in the Schwarschild geometry, I'll just add that above when you refer to "speed" you are probably tacitly assuming that speeds measured over noninfinitesimal distances have a unique meaning, if we fix an observer and a target."

    (Is there any provision for keeping a running list of posts one might later want to cite? And I obviously haven't yet learned how to cite a post I wrote in a less awkward manner--- can someone tell me what is the markup for an internal link? What is the most efficient way to obtain the numerical ID of a post?)

    I should have provided the link to the post in question earlier, but this is the topic of the post I mentioned and which I have now linked to just above.

    In this post, I explained two distinct operationally significant notions of "distance" over an extended region (one not even symmetric) and compared them quantitatively, finding that for radially separated observers the three quantities obey a fairly memorable inequality.

    Skipping ahead and jumping around is indeed the best way to get your feet wet in MTW. But the pictures I think you should be looking at occur a bit farther on, in section 31.4.

    Try the pictures in Box 31.2, which depicts infinitesimal light cones (drawn using a suitable frame field) at various events in a Schwarzschild hole. In a photocopy of the picture on p. 829, sketch a vertical line outside the shaded cylinder; this is the world line of some hovering observer. Looking at the world line labled "world line of infalling particle", you can figure out how to sketch the world line of a particle dropped by the hovering observer. At the event where the particle is dropped, its world line will be tangent to the world line of the hovering observer, but that world line is bending radially outward (in the picture, it appears straight and the falling particle's world line appears curved, but geometrically it is just the other way around!), so the two world lines diverge and the dropped particle falls into the hole in finite proper time by an ideal clock carried with the particle. But radially outgoing light signals from the infalling particle are redshifted out of existence just before it passes through the horizon, and thereafter it cannot send signals to the hovering observer, although it can recieve signals which the hovering observer sends after it into the hole for a brief time before it falls into the curvature singularity at r=0.

    Right, and from Box 31.2 that should make more sense now.

    Right.

    I don't know what you mean by "he should never worry".

    As for the information paradox, I think that is far beyond your level right now (if it's too hard, as I believe, for Hawking and other leading researchers, given the present state of physics, it's certainly much too hard for a gtr newbie!!). I'll just remind you that this involves other ideas (from quantum field theory) while lie outside the domain of classical relativistic physics, and that QFT is far more counterintuitive than gtr, so I'd advise you to focus on acquiring good intuition for the geometric features of classical black hole models.

    Chris Hillman
     
  17. Dec 5, 2006 #16
    Chris Hillman:

    Thanks, that was helpful.

    The kicker for me was the Geroch book, which arrived this weekend. It helped me a lot. I can now understand that an external observer is not completely disconnected from the space-time inside the horizon of a black hole – he can cross the horizon himself, and still encounter someone who fell in earlier, if things are arranged properly.

    On the other hand, in this situation, I’m not convinced that there ever was a horizon separating the two travelers. The observer would see every instant of his friend’s existence as the observer caught up with and encountered his friend. No light would be “redshifted out of existence just before it passes through the horizon”.

    It is hard to imagine what is going on when presented with a concrete image of a “horizon”. The horizon is really a more ephemeral thing, describing the relationship between the observer and the black hole. I’m feeling better about it now. The “twisted” space-time is still hard to imagine, but I think I am getting the flavor of it.

    I did see your earlier post on the thread Schwarzschild Metric Question and left a few comments there. (I see you’ve posted some more since then)…Jim

    PS - about embedding links - I copied the address from my browser while looking at the other thread, then used the "go advanced" option to create the link. (I think that will work). You could probably keep the resulting URL text string in a file on your machine for pasting in later posts.
     
  18. Dec 6, 2006 #17

    Chris Hillman

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    Progress toward understanding event horizons

    Good!

    Who said that "light would be “redshifted out of existence just before it passes through the horizon"? Certainly not I--- gtr doesn't say anything like that, and I don't know how you might have gotten this impression. Keep studying the Geroch book, maybe you'll figure out on your own why I objected here.

    Well, no-one said this is supposed to be easy! (I might have implied that in my post about my own first encounter with gtr, but you shouldn't assume that everyone will take to curved Lorentzian manifolds quite so painlessly.) Keep reading Geroch and keep drawing your own spacetime diagrams.

    That's basically what I've been doing to obtain a link to a post/thread, but I assume there is a one-step process, and I still don't know the proper Physics Forums markup to link to a specific post "by hand" if you don't want to quote text from it.

    Chris Hillman
     
  19. May 28, 2011 #18
    I have a "quick" question, then. Let me just say that I am a COMPLETE newb at this entire subject and that it intrigues me to no end. I don't have a "strong" mathematical background, but have normally been good at math, I just never pursued it. Due to that, I have been reading several forums on the subject of black holes in the past week. But after reading the latest posts in this thread, I have a new question that I just assumed about before.

    If the observer dropped the particle and it started on its trip toward the black hole, would the observer not lose "sight" of the particle because of the fact (or at least I think it's a fact) that light cannot exit a black hole? So the observer would not be able to receive the particle in a visual sense, correct?

    Apologies of that is completely and utterly wrong. Ha.

    Matt
     
  20. May 28, 2011 #19
    Jim: An excellent book is Kip Thorne's BLACK HOLES AND TIME WARPS. Loads of concepts explanations and diagrams, no realy math. Another is THE BLACK HOLE WAR by Leonard Susskind which features the arguments between Susskind and Hawking....and again no math....both sources very detailed and insightul.
     
  21. Jan 12, 2012 #20
    Here’s my theorey about the size of a star composed of relativistic material:

    The gravitational energy could be as low as (4GM^2)/(5R) for a typical density profile, or possibly as high as (GM^2)/R (unlikely) if the star has a high density core. The total energy creating pressure would be (Mc^2)/3. Using the viral theorem (the energy creating pressure equals half the gravitational energy), a non-rotating star of relativistic material would have a radius as small as (1.2GM)/(c^2) or as large as (1.5GM)/(c^2), or between 60 - 75% of the Schwarzchild radius.

    If this model is true, it could be verified someday by the observation of the merger of two approximately equal mass black holes: a massive ejection from the relativistic stars would occur.

    This also presents a different possible “origin” of our universe other than the big bang. Consider if two massive orbiting black holes merged, with each approximately half the mass of the universe. They would eject relativistic material for millions of years.
     
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