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Many people on Physics SE (myself included) have been confused about what black hole formation and evaporation look like when viewed from far away. For example:

Does any particle ever reach any singularity inside the black hole?

Can black holes form in a finite amount of time?

How can anything ever fall into a black hole as seen from an outside observer?

From where (in space-time) does Hawking radiation originate?

How does the evaporation of a black hole look for a distant observer?

and numerous duplicates.

This confusion all arises from the same place: the apparent contradiction between (a) the fact that a Schwarzchild event horizon lies in a faraway observer's infinite future, so from her perspective infalling matter takes an infinite amount of time to actually hit the black hole, and (b) the following naive chronological sequence:

  1. Black hole forms
  2. More matter falls into black hole
  3. Black hole grows
  4. Black hole's Hawking radiation rate surpasses rate of matter infall
  5. Black hole shrinks
  6. Black hole evaporates completely

The unifying question is, how can a faraway observer observe all six of these developments in sequence, when the first one takes place in her infinite future?

In principle, this question can be mostly or completely answered by studying this Penrose diagram that I stole from Nathaniel:

https://i.stack.imgur.com/Qtjrx.png

Unfortunately, my intuitive understanding of Penrose diagrams isn't great, what with their mixing up and rescaling of the asymptotic space and time coordinates. I think that for a situation this subtle, a picture or video is worth a thousand words. Therefore, I (and I think many other SE users) would be eternally grateful, and I think many misconceptions would be cleared up, if someone could create a simple qualitative video visualization which translates this Penrose diagram into the perspective of a faraway observer (specifically, an observer following a timelike geodesic at such large asymptotic Schwarzchild $r$ coordinate that this $r$ coordinate changes negligibly over her perspective of the black hole's entire lifetime).

I'm thinking it would look something like this: a bunch of blue dots (representing matter) initially drifting inward, appearing to get "stuck" just outside of a growing black circle representing the absolute and/or apparent horizon, then yellow dots/rays representing Hawking radiation moving outward from just outside the horizon and passing the blue does, the black circle and its surrounding "layer" of blue dots shrinking, and the blue dots and black circle all finally collapsing to a point and sending out a big shower of yellow dots/rays. However, please correct any details of my mental picture that are incorrect (and feel free to change the suggested color scheme :-) ). Please feel to speed up or slow down the time scales for visual clarity (since I suspect a realistic black hole would just sit around for a few eons and then appear to vanish in a comparative instant), but please preserve the chronological ordering of observed events. Also, assume that the observer can detect arbitrarily low-frequency radiation, to overcome the huge redshift from matter very close to the apparent horizon. Thanks!

(PS To forestall the inevitable comments: yes, I'm fully aware that from the perspective of an observer falling into a black hole, crossing the horizon only takes finite proper time, and that he does not locally observe anything unusual as he does so.)

Edit: To clarify, I'm certainly not asking anyone to do a simulation of black hole collapse under realistic assumptions about the stress-tensor, or anything like that - just to take the the Penrose diagram above and figure out the conformal mapping that turns it back into the ordinary Schwarzchild coordinates. Not necessarily even mathematically precisely, just qualitatively would work.

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tparker
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  • In my understanding time stops for matter when it reaches the event horizon, but as more matter falls in and time stops for it the radius of the event horizon will increase. (Interesting I wonder if that gives a kind of fixed density for black holes.) But I imagine you need a professional to clear this up rather than an enthusiast to hint on possiblities. – JMLCarter Feb 06 '17 at 01:33
  • oh, and btw, an external observer looses sight of objects as they descend through the photosphere, the event horizon observed from a distance is very black. – JMLCarter Feb 06 '17 at 01:41
  • Also wouldn't the rate of matter in-fall drop when the supply is exhausted? – JMLCarter Feb 06 '17 at 01:49
  • @JMLCarter Yes - that's why eventually the black hole starts to shrink and then evaporates. – tparker Feb 06 '17 at 01:52
  • That's a lot of questions, and you want somebody to do a full length movie of it. There's simulations around you can find, I have not seen one from infinity but I'd guess it looks the same just slowed. The question of whether the real event horizon forms or it's an apparent horizon didn't bother anyone much till the information paradox surfaced, and the working assumption is mostly that you can get close enough to a real event horizon to not know the difference, maybe it's an apparent horizon but no matter. At infinity you will see someone entering the horizon at the same time -continued – Bob Bee Feb 06 '17 at 05:23
  • @BobBee Well, I won't insist it be full-length, since I understand that black holes are expected to last for trillions of years :) . I edited my post to clarify that I'm just looking for a completely qualitative visualization, not any kind of actual numerical simulation. – tparker Feb 06 '17 at 06:03
  • Continued - you see it evaporate away finally, because that's when the time dilation stops. As for similations, there are plenty, the ones for the merging black hole are very good. For black holes Google black holes simulations. There's quite a few, go with ones from sites like Hubble, or JILA, LIGO, CalTech, or other well known places. – Bob Bee Feb 06 '17 at 06:12
  • For the merging black holes, it's amazing how fast the last phase of the merger took place, you see it in the simulation from LIGO. – Bob Bee Feb 06 '17 at 06:18
  • And Hawking radiation to the extent one can localize it (quantum wavelength) has to look like it's coming from outside the horizon, you would not see anything coming from inside - it's like quantum tunneling or induced emission (Hawking did his calculations as a quantum field in the external Schwarzschild metric close to the horizon, and got outgoing and Ingoing field perturbations, i.e. particles, and they were still there for the vacuum quantum field, i.e., vacuum perturbations). – Bob Bee Feb 06 '17 at 06:29
  • Please note that energy of evaporation by Hawking radiation goes inversely with the mass of the black hole, http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html " if the mass of a black hole is M solar masses, Hawking predicted it should glow like a blackbody of temperature 
                     6 × 10^-8/M kelvins, "The frequencies of such a black body radiation are too small to generate other than massless particles, i.e. photons
    – anna v Feb 06 '17 at 11:32

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