To my knowledge if you calculate the coordinate time (time experienced by an observer at spatial infinity) it takes an infinite amount of time for an object to fall past the horizon of a Schwarzschild black hole. Doesn't this imply that it takes an infinite amount of coordinate time for a Schwarzschild Black Hole to form since the last bit of in-falling matter won't ever ross the horizon as observed by someone at spatial infinity? If so, is it possible for other types of black holes (Kerr etc.) to form in finite coordinate time?
Pick some maximum visible wavelength of light (say, the radius of the solar system). And let's consider only initial source frequencies below the rate at which, say, one photon per year is emitted. In a finite time, all of the light leaving the matter distribution below this frequency, as observed by a distant observer, will be redshifted beyond your maximum wavelength. It will appear practicably indistinguishable from a black hole.
The actual plunge phase of this process will happen very, very quickly (think days, not centuries), so the object will go from emitting in the visible to essentially dark in a very short period of time.
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