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Since we are external observers, an object falling in a black hole should take an infinite amount of time right? If so, what is the answer to my question in the title?

Qmechanic
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Christian Pao.
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  • But doesn't an object take an infinite amount of time to fall in a black hole? – Christian Pao. Jul 27 '16 at 23:22
  • Maybe photons that are captured by the blackhole do take an infinite amount of time to fall in although I doubt it. The light that we see evidently escaped so it's not part of that process and would come to an end. – Bill Alsept Jul 27 '16 at 23:27
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    Possible duplicate of Can black holes form in a finite amount of time? – Diracology Jul 27 '16 at 23:28
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    Possible duplicate of http://physics.stackexchange.com/q/21319/ have a read of this answer. –  Jul 27 '16 at 23:31
  • See e.g. http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html. The time it takes for an object to dim is only a few times larger than the classical fall time would be, in other words, once things get close, they are gone very quickly. – CuriousOne Jul 28 '16 at 00:55
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    It's a shame this is closed since I think there is actually a correct answer that is really not addressed at all by either of the so-called duplicate questions/answers. The practical answer is that material disappears extremely quickly once it reaches the ISCO and so it is the time to reach the ISCO and the timescales for tidal disruption and the transfer of angular momentum in the consequent accretion disc that are important. – ProfRob Jul 28 '16 at 11:37

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While something falling into a black hole doesn't pass the horizon in a finite time, as calculated by an outside observer, the things that have fallen in become unobservable very shortly after they approach the horizon. This is because the redshift from somewhere near the horizon is so large that the photons have an enormous wavelength, and are thus unobservable. The timescale for falling-in matter to be redshifted to invisibility is a small multiple of the time it would take light to travel a distance of $r$, where $r$ is the radius of the black hole. This is on the order of milliseconds for a solar-mass black hole, and hours for the supermassive black holes at the centers of galaxies.

When a real black hole eats a star, how long do we observe this process happening? I expect the number varies greatly depending on the size of the black hole, and the details of how it eats the star. This website says we have actually seen a star being eaten by a black hole. Or at least, the star was ripped apart by the black hole and some of it was eaten. It took around a year. But it took this long not because of the infinite time the star took falling into the black hole once it came close to the event horizon, but because the star was orbiting the black hole, relatively far from the event horizon, while it was being ripped apart.

Peter Shor
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  • Beautiful video. Anyway, wouldn't some gas which got ripped apart by the black holes virtually freeze near the even horizon? Or would "all" the gas rotate with the black hole until it gets released through hawking radiation? – Christian Pao. Jul 28 '16 at 00:47
  • @Christian: The question was about what we can see. We can't *see* any of that, because any radiation emitted from near the black hole horizon is redshifted so much as to be undetectable. – Peter Shor Jul 28 '16 at 00:57
  • Ohh right, I was forgetting about that. Is there a limit to how much an object would be redshifted? Can it reach the wavelength of the cosmic microwave background(which would mean that what was a star before, literally mixed with the cmb becoming... nothing)? – Christian Pao. Jul 28 '16 at 01:07
  • Light coming out of a black hole can be redshifted far more than that. A black hole probably can't emit light of wavelengths much larger than its radius, so that would be the limit of the redshift. – Peter Shor Jul 28 '16 at 14:09
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Well theoretically, the answer to your question would be infinite amount of time, but practically, it would take longer than the actual duration of the event due to slow down of photons. If it was really infinite time, then we should be able to see history of all the falls since a black hole was first formed, which obviously is not true today. Not only that we would be able to see it now, but also we should be able to do so for an infinitely long time in future. Once a photon leaves from near horizon, it would pick up speed pretty fast and should not take that long for the photons to disappear.

Even if there some are photons that take infinitely long time, they would not be sufficient to form the "being Eaten" image for a very long time. I guess we need some minimum number of photons per second to form a continuous image.

Looking at it in another way, If there are certain number of photons crossing the surface of the sphere, for an infinite long time, it would require infinite amount of energy just in terms of light.

kpv
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  • Do you have sources? Actual numbers? What distinguishes this answer from baseless, unfounded speculation? – Peter Shor Jul 28 '16 at 00:33
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    That is pretty much completely false. See e.g. http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html – CuriousOne Jul 28 '16 at 00:53
  • @Peter Shor: I did mention theoretically it is infinite amount of time. In practical, irrespective of theory, don't we need a minimum number of photons to make a picture of the event? That minimum number of photons in your view (and in all possible view), forever, wouldn't it amount to infinite amount of energy? Where the energy will come from? If we look at any black hole today, do we really see all events of past? If we don't, then what happened to the infinite tme theory? The infinite time theory has assumption of infinite photon source. Isn't it? – kpv Jul 28 '16 at 03:26
  • @CuriousOne: and Peter Shor, please see above comments. In addition, the object that fell into black hole is long gone past the horizon. What is left is just the photons created till the body crossed EH. Now, how can we spread those finite number of photons in all the view for infinite amount of time? I can not think of a way. Could you please explain. Note that we have to be able to make a picture of the event in all possible view, not just in your view. Because we can not focus photons only in your direction, they will escape in all directions (may be half sphere, if not full). – kpv Jul 28 '16 at 03:32
  • @CuriousOne: and Peter Shor, I assumed when you say it is wrong/baseless, you meant it would take infinite time. Because, my answer is that it can not be infinite time. If you did not infinite time, then please clarify and I will edit/delete. – kpv Jul 28 '16 at 03:42
  • I agree it's not infinite time. But you said "very long time", which is wrong by most scales of "very long". That's what I meant by "baseless speculation". Rereading your answer more carefully, I'm even more confused. You say "long time" at one spot, "not take that long" at another spot, and "very long time" at a third spot. Does this mean milliseconds, seconds, hours, days, years, centuries? The only actual content in this answer is "not infinite". – Peter Shor Jul 28 '16 at 13:55
  • @Peter Shor: I am editing it. – kpv Jul 28 '16 at 16:56