The well-known fable of an astronaut sending signals out to an external observer while falling toward an event horizon states that the time lapse between such signals becomes greater even if in the astronaut sends them out periodically (as judged in his inertial frame). When viewed from earth and weighing time-dilation due to the gravitational field of the collapsing star, how is it possible that a black hole can form in finite time (for any external observer) if it takes an infinite amount of time to "see" events occurring at the event horizon?
Similar questions have cropped up on this site many times, and the debate surrounding them is usually fractious because people misunderstand each other's use of words like exist.
One of the lessons of General Relativity is that any observer has to choose a locally convenient coordinate system that may not be globally convenient. We on Earth (quite sensibly) choose time as measured on our clocks and distance as measured by our rulers, and these coordinates are known as the Schwarzschild coordinates (strictly speaking they are shell coordinates, but the difference at the orbital distance of the Earth from the Sun is negligable). Locally our coordinates work very well, but when the central body is a black hole the coordinates become increasingly curved as you approach the event horizon and at the event horizon they fail completely resulting in a coordinate singularity.
I've made this sound like a mathematical nicety, but it's quite real. Remember that by the time coordinate I mean the time we measure on our clocks, and that means there is a singularity in our measurements of time at the event horizion. This is why it takes an infinite time for anything to reach the event horizon, let alone cross it.
The question is whether it is therefore correct to say that: the event horizon never forms. It is quite true that you and I and everyone outside the black hole will never measure the time the event horizon forms, because it would take an infinite time. However there are lots of coordinate systems that have no singularity at the horizon, such as Gullstrand-Painlevé, Eddington-Finkelstein and Kruskal-Szekeres coordinates. The trouble is that these coordinates are somewhat abstract and do not coincide with the experience of any human observer. However since such coordinates exist, physicists tend to be quite comfortable stating that black holes form even if human experimenters could never observe it.
It's a matter of what you mean by "see". Even for a distant observer, it will take a small amount of time for the gravitational redshift effect to become essentially infinite. If your collapsing gas star redshifts to the point where it won't emit a single photon in the age of the universe, it may not have yet technically "redshifted to zero", but it has functionally redshifted to zero as far as experiment is concerned.
The actual picture seen by an external observer is consistent with the general picture described by a naïve interpretation -- a black object that is not emitting anything other than (what is, for macroscopic holes, a vanishingly small amount of) Hawking radiation, that will absorb objects that enters it. I should also add that the apparent horizon of a collapsing star will move outward at a speed faster than the speed of light, which will solve the infinite redshift issue, as well.
The short answer is infinity.
The elastic body model, resulting from the work of Milo Wolff and Gabriel LaFreniere and Jeff Yee, says that the elementary particle is a pulsating soliton in a medium that is non-linear. The non-linear medium has an absolute density (analogous to the curvature of space-time), instead of a purely abstract amplitude, and Hook's law applies in it - it reacts to compression with opposing force - this is something that is missing in Einstein's GTR, and this is his biggest mistake in this matter. What he said about GTR, saying that the GTR is not full.
Well, the biggest absurdity arising from this theory - black holes - is just a consequence of not taking into account the internal pressure of space, which is an obvious component of every classic elastic body.
The collapsing star first breaks the pressure inside the atoms, then inside the neutrons, until it disappears in singularity. However, most thinkers do not take into account the fact that the same pressure that prevents atoms and neutrons from collapsing will also stop the entire star from collapsing. This is because both the individual material particles and the gravitational field around the star consist of the density of the same substance - space-time at Einstein, flexible space at Wolff, Aether at LaFreniere and Jeff Yee.
Also we must remember the atomic and electromagnetic forces are much more powerful than gravitational forces.
Noting by Haramein, then by Gabriel LaFreniere (probably also by others :)) that the energy contained in the volume of the proton / electron is enough to make it a black hole, points to an important issue - well, according to the model of the elastic medium, each the material particle is a kind of black hole - looking at how much energy it has. It arises where, within a given area, the density of Ether exceeds a certain critical value. However, this will not lead to the collapse of this area, but to its transformation into a soliton - a creature that can sustain its own existence. What feeds him? Waves around it, called by scientists quantum fluctuations, or vacuum energy, relict radiation, etc.
Vacuum has its energy, some have called it background relikt radiation others have the lowest energy state. Vacuum thickens to form a temporary unstable soliton - what others have called quantum fluctuations.
That is why the equation of the black hole needed to include the vacuum energy it contained. For the same reason, Jeff Yee had to put a constant density of ether in the equation of photon and electron energy.
This is remarkably coincident with Tesla's belief that matter 'absorbs' the Ether to exist.
So the same mechanism that causes matter to exist also excludes black holes. Aether density will always take energy, bend the paths of other densities and waves, but it will never collapse because it will have internal pressure. This is a direct consequence of the characteristics of a classical elastic medium.
The same mechanism contained in the elastic body model is responsible for the process of absorption and emission of an electromagnetic wave by an atom (a soliton made from of other solitons). Soliton aims to return to its ground state - stable state.
Einstein did not suspect that his confusing space-time could be replaced by something so simple. However, physicists who perceive the wave nature of matter are easier because the physical wave, despite the trumpeting, requires a medium.
The unequivocal experimental proof of the wave (frequency) nature of matter is the electron image recorded in 2007. This image was recorded by a team of Swedish scientists from the University of Lund. The image turned out to be a soliton image in line with the proposals of Milo Wolf and Gabriel LaFreniere published in the years 1998 - 2002:
Sorry for My English.