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twhites
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I think this subject may have been discussed here already; please point to the thread if so.
I am unable to understand how Black Holes can form within the lifetime of the universe.
If nothing can cross an event horizon in finite time, then it seems clear that the horizon can't form (at least by a collapse mechanism; is there another way?) in finite time either. It seems to me that several arguments can be made that nothing (even light) can, in fact, cross an event horizon in a finite time (as we on Earth, i.e., far from the BH) would measure it.
I am aware that an object falling on a radial trajectory will cross an event horizon in finite proper time. But that is not the time that a far-field observer (ffo) uses, not only because he/she is in flat space-time, but because he/she is stationary w.r.t. the horizon. It appears to me that even the clock of a momentarily stationary observer near the horizon runs very much more slowly than that of the ffo (in the limit of r=2M, infinitely so). Conversely, the clock of the ffo runs faster than that of the poor soul near the horizon (again, infinitely so at r=2M). This statement is, I believe, equivalent to the observation of the gravitational red-shift/blue-shift of light exchanged between the two observers, which I understand to diverge as stated (in both directions).
Likewise while the proper distance between the ffo and the horizon is finite, this distance is not directly measurable (it is, after all, space-like). We measure distance by timing light transmission times, so the measured distance from the ffo to the horizon is determined by (say) measuring the time it takes for a light pulse emitted by the ffo to be reflected and returned to the ffo by a (momentarily stationary) observer near the horizon. This time diverges as r->2M; it is certainly the case that at r = 2M, no such light pulse ever returns to the ffo. This appears to me to mean that (even) light can't reach/cross the horizon in finite (far-field) time. The difference between this distance and that measured by the inertial observer (falling on a radial trajectory) I interpret as the result of a large Lorentz contraction; the inertial observer is moving at a velocity (relative to the ffo and the horizon) close to (approaching) c as he/she approaches r=2M.
What's wrong with these arguments? It seems to me to give a picture with certain benefits, since it avoids the necessity of worrying about what happens inside an event horizon--there is no such volume. There would appear to be no entropy-loss problem either.
I am unable to understand how Black Holes can form within the lifetime of the universe.
If nothing can cross an event horizon in finite time, then it seems clear that the horizon can't form (at least by a collapse mechanism; is there another way?) in finite time either. It seems to me that several arguments can be made that nothing (even light) can, in fact, cross an event horizon in a finite time (as we on Earth, i.e., far from the BH) would measure it.
I am aware that an object falling on a radial trajectory will cross an event horizon in finite proper time. But that is not the time that a far-field observer (ffo) uses, not only because he/she is in flat space-time, but because he/she is stationary w.r.t. the horizon. It appears to me that even the clock of a momentarily stationary observer near the horizon runs very much more slowly than that of the ffo (in the limit of r=2M, infinitely so). Conversely, the clock of the ffo runs faster than that of the poor soul near the horizon (again, infinitely so at r=2M). This statement is, I believe, equivalent to the observation of the gravitational red-shift/blue-shift of light exchanged between the two observers, which I understand to diverge as stated (in both directions).
Likewise while the proper distance between the ffo and the horizon is finite, this distance is not directly measurable (it is, after all, space-like). We measure distance by timing light transmission times, so the measured distance from the ffo to the horizon is determined by (say) measuring the time it takes for a light pulse emitted by the ffo to be reflected and returned to the ffo by a (momentarily stationary) observer near the horizon. This time diverges as r->2M; it is certainly the case that at r = 2M, no such light pulse ever returns to the ffo. This appears to me to mean that (even) light can't reach/cross the horizon in finite (far-field) time. The difference between this distance and that measured by the inertial observer (falling on a radial trajectory) I interpret as the result of a large Lorentz contraction; the inertial observer is moving at a velocity (relative to the ffo and the horizon) close to (approaching) c as he/she approaches r=2M.
What's wrong with these arguments? It seems to me to give a picture with certain benefits, since it avoids the necessity of worrying about what happens inside an event horizon--there is no such volume. There would appear to be no entropy-loss problem either.