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Black hole question: apparent rate of growth as seen by external observers

  1. Dec 7, 2005 #1

    JesseM

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    Suppose we have an observer at a large distance from the event horizon of a black hole, pouring matter towards the BH at some constant rate of m per second. Will he see the BH's radius increasing at a rate of 2Gm/c^2 per second, or does gravitational time dilation change the apparent growth rate somehow?
     
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  3. Dec 7, 2005 #2

    Physics Monkey

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    This is a tricky question because in the Schwarzschild solution, for example, any infalling mass will take infinite coordinate time, as judged by an external observer, to reach the horizon. So how can the hole grow if matter can never enter it? The same thing is true for two black holes that merge: it seems that their event horizons have to actually touch for all time. Of course, no one knows an exact solution in this case so maybe this reasoning is flawed. You can get energy out of Kerr type hole with something like a Penrose process, but I don't see how this helps understand how black holes can grow. In my personal opinion, I think it may be that we need to understand black holes that don't require future and past infinity in the spacetime.

    However, I may be way off base here, advanced black hole theory isn't exactly my specialty. Perhaps the problem is alleviated in quantum gravity, that would certainly be interesting, though I see no reason to suspect a classical GR explanation isn't possible.
     
    Last edited: Dec 7, 2005
  4. Dec 7, 2005 #3

    pervect

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    An interesting question. I don't see how the external observer is going to measure the location of the event horizon - for instance, he won't get a radar echo from it...

    Suppose the observer instead decides to find the mass of the black hole to compute the location of the horizon. He could observe orbital parameters of an object orbiting the hole. He may be far away from the hole, but he could observe the orbital parameters of an object "close" to the event horizon, I suppose. Close would have to be within the area that stable orbits existed - definitely outside the photon sphere, for instance - so there wouldn't be any huge gravitational time dilation effects.

    So I think he's going to get the mass of the black hole plus the mass of some of the stuff outside the hole, I don't think he's going to get a pure measurement of the mass of the black hole. At least that's my first reaction.
     
  5. Dec 7, 2005 #4

    JesseM

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    Is there any particularly "natural" coordinate system to use in the case of a growing black hole, perhaps one that would reduce to Schwarzschild coordinates for brief time intervals when the size wasn't changing appreciably? If so, the question could be rephrased as one about how the event horizon is growing in such a coordinate system, instead of one about what the observer will actually see.

    Incidentally, the question arose in the context of a discussion on another board of what would happen if a small black hole fell to the center of the earth--someone suggested that perhaps we wouldn't have to worry about it gobbling up the entire planet, since from our external POV matter would never reach the event horizon so the black hole would never grow in size. This is definitely incorrect, no? There must be some meaningful sense in which we can observe the size of a black hole to change over time, otherwise the concept of black hole evaporation via Hawking radiation wouldn't make sense.
     
  6. Dec 7, 2005 #5

    Physics Monkey

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    For a true classical Schwarzschild black hole, infalling matter will never reach the event horizon as judged by an external observer, it just won't. But then significant infalling matter isn't going to be described by a Schwarzschild solution anyway. If we take as given that "real" black holes can grow by absorbing material, then these holes must have a rather different topological structure than the usual Schwarzschild hole, right?
     
  7. Dec 7, 2005 #6

    JesseM

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    I realize an external observer can never see anything reach the horizon, but can't the size of the horizon itself change, carrying the near-frozen images of objects near the surface (assuming you could still see them at arbitrary redshifts) with it? Something like this seems to be what's described in this FAQ answer on black hole evaporation, where they say an external observer would see an infalling object keep hovering closer and closer to the horizon as the horizon itself shrinks, finally reaching the horizon at the precise moment the black hole shrinks to nothing.
     
  8. Dec 8, 2005 #7

    JesseM

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    I had a memory that Kip Thorne's book Black Holes & Time Warps had a discussion of what happens when a black hole swallows something and the size of its event horizon changes, so I went back and checked, it's discussed in chapter 12, which starts on p. 413:
    And Box 12.2 provides an example of how the apparent and absolute horizons change in response to matter falling into the black hole:
    So, is anyone familiar with these notions of the apparent and absolute horizon of a black hole? When matter is being fed into the hole continuously as in my original question, I'd think the apparent horizon would move outward continuously rather than jumping discontinously--I wonder if it would simply coincide with the absolute horizon in this case, or if they would both move outward continuously but one would lag behind the other. And, as in my original question, if the mass were dropping in at a rate of M per second (as seen by a distant observer), I wonder if either one or both of the apparent and absolute horizons would grow at a rate of 2GM/c^2 per second.
     
    Last edited: Dec 8, 2005
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