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How do black holes grow?

  1. Nov 17, 2012 #1
    A lot of scientific literature states that black holes 'grow' in size (which I think is equivalent to saying 'grow their Schwarzschild radius or event horizon'). They apparently do so by consuming external matter that falls into them.

    However, any matter that does fall toward a black hole, and gets close to the event horizon, should never actually reach the event horizon in the lifetime of the Universe?

    I am talking about the point of view of any observers outside the even horizon (e.g. us), not observers who fall into the black hole (who could cross the event horizon in their lifetimes and not even notice the event, ignoring the physical discomfort or deformities caused by tidal forces).

    Given the above, how can black holes ever 'grow' in the lifetime of the Universe? (Assuming that some of them have existed from the beginning of the Universe for some reason)
     
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  3. Nov 17, 2012 #2

    PeterDonis

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    Yes, that's correct.

    The phrase "in the lifetime of the Universe" is coordinate-dependent, and can lead to confusion. A better way to describe what's happening would be to say that light from events at or inside the EH can never get back out to a distant observer. See below for further comment.

    We've had a number of threads on this. You agree that observers who fall into the BH can cross the event horizon in a finite time according to their own clocks, i.e., in a finite proper time. Therefore, matter that falls into the BH can also reach the horizon in a finite proper time. That's all that's necessary for the BH to grow.

    It is true that no light signals from any event at or inside the horizon can get back out to the rest of the Universe, as I said above; so an observer far away from the hole will never see anything cross the horizon. If an observer far away from the hole tries to describe the spacetime using the time coordinate most natural to him, he can only describe events from which light signals can reach him; that means that he can't use the time coordinate most natural to him to describe events at or inside the horizon. But that doesn't mean such events don't exist; it just means the distant observer can't describe them using his most natural time coordinate.
     
  4. Nov 17, 2012 #3
    Thanks for the better description of what I was trying to say.

    Now, given your above statement, doesn't it mean that an observer far away can also never see the event horizon of a black hole grow, no matter how long he lives?

    This is where I am trying to get some clarity on what it means for a black hole to 'grow'. (a) The notion seems to imply that a very long-lived observer would be able to at some point say that a certain black hole's even horizon has a radius of 'R' and some time later (by his natural time) that the same black hole's radius is now 'R + ΔR'. But (b) it appears that he cannot do so, because he would never see any matter reaching the event horizon to help the black holes mass (and therefore event horizon) grow.

    I am not able to mentally reconcile these two (a) and (b), somehow. I am partial to the point of view of the observer far away from the event horizon rather than the one crossing it, as I am identifying ourselves with the observers of the first kind.
     
  5. Nov 17, 2012 #4

    PeterDonis

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    If you mean "see" as in "receive light signals from", then no. However, the faraway observer does receive other evidence that the BH has gained mass; he feels an increased gravitational field.

    The key phrase here is "by his natural time". Yes, by his natural time, he never "sees" the BH grow, because his natural time simply can't describe that part of the spacetime, the part at and inside the horizon. But that doesn't mean the part of the spacetime at and inside the horizon doesn't exist, or that matter can't fall into it.

    We *are* observers of the first kind, so it's natural that you would identify us with such observers. However, you need to be careful not to be too "partial" to the point of view of such observers, because the most natural "point of view" for such observers can't describe a portion of the spacetime (at and inside the horizon), so that point of view is a limited one.
     
  6. Nov 17, 2012 #5

    PAllen

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    The observer outside always 'sees' a very near black hole, with an 'almost horizon' (note, this 'almost horizon' is blacker than anything else in the universe in finite time for the external observer - however, technically, it has not quite become a horizon as seen by the outside observer. When more matter falls in, the outside obsever sees the 'almost horizon' grow. So everything is always an 'almost black hole' as seen by an outside observer.

    However, you can't call it relativity an claim there is only one allowed type of observer. Further, as with all cases of getting light, you make deductions about what has happened where the light was emitted, since it was emitted. If you ask these question, you have no choice but to consider there is a black hole horizon and singularity, and new matter falls through the horizon and reaches the singularity in finite time. GR tells you that the light you see coming from a collapsed object is exceedingly ancient light - so you ask what happened since it was emitted, for the object itself. GR has only one answer to this - if became a singularity, even though you will never see this.
     
  7. Nov 17, 2012 #6
    Yes, "detect" would be a better description.

    This is where the crux of my question is.

    Then we should never be able to see in our (very extended) lifetimes the creation of a black hole from a massive star's collapse? But apparently that does happen to be observable even in our normal human lifetimes, and certainly if our lifetimes were imagined to be of the order of very long-lived stars...

    This I agree and have no issues with. My questions are entirely from the external observer's point of view, and what they can detect in an ambrosia-extended lifetime.

    Agreed from the perspective of "seeing". I have modified this to "detecting" as above. My point is, the external observer will not be able to detect the 'almost horizon' grow unless the actual event horizon also grows, with matter crossing the event horizon in the external observers extended lifetime (eliminating the trivial situation of matter density increase in the space around a black hole because of its strong gravity, even without such matter crossing the event horizon from an external perspective).

    Agreed, but I believe it is valid to ask a question from the point of view of one of these observers. In this post I am looking at it from the external observers point of view.

    This is where the issue is... from an external observers point of view, new matter cannot fall through the horizon in (his/hers) finite time. Or are you saying that is wrong?
     
    Last edited: Nov 17, 2012
  8. Nov 17, 2012 #7
    The distant observer sees (in a theoretical sense - he can't really see any of this) the contracting mass get more and more time-dilated as it approaches to being a black hole. It will never become a black hole in his time-frame. Further matter falling in will freeze around this matter, continually edging closer and closer, more and more slowly, so that a whole volume around the gravitational radius is effectively frozen.

    As this happens, the gravitational radius of the total mass will increase, but the mass within any particular radius will always be just insufficient to form an event horizon at that radius. We end up with a growing region of almost-event-horizon.

    So as more mass falls in, the external observer "sees" the almost-horizon grow, but there is no proper horizon to grow within it, just a whole contained region of almost-horizon.

    Mike
     
  9. Nov 17, 2012 #8

    Bill_K

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    arindamsinha, You have a valid point. Discussions about a particle falling into a black hole and never reaching the horizon r = 2M typically assume that the particle is a test particle with mass negligible compared to the mass M of the hole. But it's important to realize that the horizon relates not to the local gravitational field, but to the gravitational field at infinity. It's the radius from which light rays cannot escape to infinity.

    If you drop a mass ΔM into the hole, by Gauss's Law the field at infinity becomes that of a mass M + ΔM, and it does not have to wait to do this until the particle arrives at r = 2M. At a given radius, the field will be changed as soon as the particle is within that radius. An outside observer will receive light rays propagating in this greater field, and will never see the particle fall beyond the new horizon, r = 2(M + ΔM).
     
  10. Nov 17, 2012 #9

    PAllen

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    I don't know what you mean here. They will see the almost horizon grow (visually, a black shadow against the sky surrounded by Einstein rings will be seen to grow. As for gravitational mass, the orbits of satellites of the BH will be different from before. Thus, no part of your statement makes sense to me.
    Of course it is valid to ask what any observer sees or measures. But it absurd, in relativity, to claim that what one type of observer sees defines the complete reality. An observer in a uniformly accelerating rocket sees part of the universe freeze and stop, forever, as long as they keep accelerating at, e.g. 1 g. Not only see, but this applies to all signals and measurement methods available to the accelerated observer. Do we conclude that this says anything about reality for that part of the universe?
    The external observer never sees it actually cross the horizon. They do see and detect the central mass growing. They can ask what their theory predicts about this region they see as frozen - just as the rocket observer can ask what theory predicts about the part of the universe that looks frozen to them.
     
  11. Nov 17, 2012 #10
    Correct me if I am wrong, but this is more the Newtonian/classical view of a 'black hole'. Light rays cannot escape to infinity, and must fall back into that radius/horizon, because the escape velocity is higher than c. However, light rays can go some distance outside the radius/horizon before falling back (and therefore be observed by someone who is close by).

    I had this notion for a long time myself, but later came to learn (correctly I hope), that according to GR, that even light rays cannot ever cross back into outer space once they have reached the event horizon. All possible paths (worldlines?) inside lead towards the singularity.

    Would love to know if this understanding is correct.

    This is true for a give region of space, within a certain radius around an arbitrary origin, irrespective of whether it contains a black hole or not.

    However, it there is a black hole, and the radius we are talking about is the event horizon, the 'as soon as the particle is within the radius' event will never happen for an external observer, no matter how long he waits for it. That is the point I am trying to bring out.
     
  12. Nov 17, 2012 #11
    That would be true of a large galaxy as well, as its gravity captures interstellar matter.

    For a black hole, an arbitrary region around it (radius > event horizon) can increase in mass and show the above effects as well.

    But what of the region of space within the event horizon itself? Since external matter can never reach it, that region can never grow more massive, as seen/detected/computed from an external observer's point of view, I believe.

    I am not at all making that claim. I understand that reality may be seen differently by different observer.

    I am just looking for an explanation from one particular point of view - how does an observer outside black holes ever see/detect/compute that a given black hole's event horizon is growing, when he cannot see/detect/compute any matter ever reaching the event horizon?

    This seems to state that the event horizon of a black hole never actually grows, from an external observers point of view. However, as more and more mass falls towards the black hole's event horizon, a sufficiently distant observer would notice the mass and gravity of that region increasing. Is that what you are saying?

    I am not talking theory here. Lot of astronomical observations have established with reasonable certainty that black holes exist, and they 'grow' by 'eating' external matter - a growth that happens even in as short a period as a human lifetime.

    Are you saying that the event horizons of these objects don't actually grow, but they accumulate more and more mass just outside the event horizon, from an external observers point of view?
     
  13. Nov 18, 2012 #12
    The problem with this thinking is that it assumes we already have a Black Hole and event horizon. But according to the O-S model, it takes an infinite time for the matter to collapse within its Schwarzschild radius, as far as a distant external observer is concerned. So there is no event horizon to grow, just an area of almost-event-horizon to expand.

    Astronomical observations could not observe the difference between such an eternally collapsing object and a fully-formed black hole. Time dilation only becomes extreme very close to the SR. With a 10km black hole (3 times the sun's mass), time dilation 1cm away from the event horizon would only be about 1000:1. In addition, the super-massive objects in some galaxies have been observed to have magnetic fields, which rules them out as black holes. So while to all intents and purposes there are black holes in the centres of most, if not all galaxies, in fact according to our clocks and theories they are not quite there yet.

    Mike
     
    Last edited: Nov 18, 2012
  14. Nov 18, 2012 #13

    PeterDonis

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    Which does not mean that the event horizon does not form. It just means that light signals from its formation never get back out to the distant observer.

    Another way of putting it: claiming that the event horizon never forms because "it takes an infinite time as far as a distant external observer is concerned" is equivalent to claiming that the region of spacetime in which the distant observer's time coordinate is finite is the entire spacetime. This claim is false.
     
  15. Nov 18, 2012 #14

    PeterDonis

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    In order to make any sense of this, you would have to have a model of an "eternally collapsing object" that was different than the standard one, so we could verify that both models make the same predictions, at least within our current accuracy of observation. AFAIK no one has come up with such an alternate model. Otherwise you're just saying that we have only one model and therefore only one set of predictions.
     
  16. Nov 18, 2012 #15

    PeterDonis

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    No, it doesn't; it just means that if they're black holes, they're not black holes surrounded by vacuum; they're black holes surrounded by clouds of plasma, which is the currently accepted model. (They're also spinning black holes in the currently accepted model, and their spin induces spin in the plasma, which is what generates the magnetic fields.)
     
  17. Nov 18, 2012 #16

    PeterDonis

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    You are equating "see/detect/compute", but they're not equivalent; the distant observer cannot "see/detect" the event horizon forming (because light signals from its formation will never reach him--that's the *definition* of an event horizon), but he *can* "compute" that it forms. That's the whole point of doing computations of gravitational collapse, by solving the Einstein Field Equation. Those solutions "compute" unequivocally that an event horizon *does* form, and that the proper time experienced by an infalling object from any finite radius outside the horizon, to reach the horizon, is finite.
     
  18. Nov 18, 2012 #17
    That's what I was thinking after seeing Mike Holland's response.

    That would be a way of getting around the question I have asked. If ideal Black Holes never actually get fully created, but certain regions of space containing matter keep getting closer and closer to the ideal, then there is no reason for them not to be able to grow. The event horizon actually never gets created!

    Still, I have not seen this theory anywhere. Is that what the 'O-S model' states? What is the 'OS-model', in brief, to explain to a layman like me?
     
  19. Nov 18, 2012 #18
    I understand that. There seemed to be too many issues coming up between the terms "see", "detect" and "compute", so I was trying to combine them to state what I mean.

    In some senses, "see" may be possible, as explained by the growing shadow.

    "Detect" is possible through measuring the gravity growth.

    "Compute" is of course possible, based on current theory.

    Let us then drop "see" and "detect". My contention is that current theory (GR), does not even allow "computation" of any external matter reaching an event horizon in finite time, from an external observer's point of view, thus the event horizon cannot even be "computed" to be growing from that perspective.

    I hope that makes it a little clearer on what my question is.
     
  20. Nov 18, 2012 #19

    PeterDonis

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    The word "never" in this context doesn't mean what you think it means. :wink: All it means here is "the black hole never gets created at any finite value of the Schwarzschild time coordinate". It does *not* mean "the black hole never gets created, period". That's because the region of spacetime that is covered by finite values of the Schwarzschild time coordinate is not the entire spacetime.

    No. As I said, there is no alternate model of an "eternally collapsing object" in which a black hole never forms (where I'm now using "never" in the strong sense, meaning "never anywhere in the spacetime).

    "O-S" stands for "Oppenheimer-Snyder"; in 1939 Oppenheimer and Snyder published a paper that modeled the collapse of a cloud of "dust" (which is a term for an idealized cloud of matter with zero pressure) under its own gravity, using General Relativity. Their basic model is still valid as a highly idealized (zero pressure in the matter, as I said, and perfect spherical symmetry) qualitative picture of gravitational collapse; it is discussed in most of the major GR textbooks (including Misner, Thorne, & Wheeler, which is where I first learned about it), and in the popular book Black Holes and Time Warps, by Kip Thorne.

    For our purposes here, the key point is that this model predicts that the spacetime *does* contain an event horizon and a black hole region. What happens is that the outer surface of the collapsing matter, as it gets smaller and the matter gets denser, eventually becomes a "trapped surface" (this is a modern term and was not used in the original Oppenheimer-Snyder paper); that is, it is a surface from which even outgoing light (light emitted directly radially outward) does not move outward (that is, it doesn't move to a larger radius). Once this happens, the collapsing matter is doomed to continue collapsing all the way to infinite density and infinite spacetime curvature at r = 0, leaving behind an event horizon and a black hole region inside the horizon.

    (Actually, the original Oppenheimer-Snyder paper, I believe, did not carry the analysis beyond the instant when the trapped surface forms; in other words, their original analysis was incomplete. But later work has confirmed their analysis and carried it to completion; the result is what I described above.)
     
  21. Nov 18, 2012 #20

    PeterDonis

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    Then I'm a bit unclear on your definition of "compute". Read my previous post describing the Oppenheimer-Snyder model; to me, this is a "computation", done by a "distant observer" (after all, that's what we are on Earth relative to any black hole in the universe), which shows that an event horizon *does* form. Why would this not count?

    (Or perhaps the problem is the phrase "from an external observer's point of view". The computation I describe shows that no light signal from at or inside the horizon will ever reach the external observer; equivalently, it shows that the region of spacetime in which the external observer's time coordinate is finite does not contain the event horizon or the black hole. If this means the EH doesn't form "from the external observer's point of view", then that's fine, but you have to be very careful not to extend that claim into "the EH doesn't form, period", which is false; the spacetime *does* contain an event horizon and a black hole, and additional matter *can* fall through the horizon and into the black hole. So adopting the "external observer's point of view" forces you to walk a very fine line, to avoid claiming too much. In my experience, most people are not able to walk that line, so it's better, IMO, to just say flat out that the event horizon and the black hole *do* form, and that the "external observer's point of view" is the wrong one to use. But your mileage may vary.)
     
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