How can any matter contract to its Schwarzschild radius if gravitational time dilation clearly states that all clocks stop at that point. So any contraction any movement would stop. If that is so why all this talk about objects which can never form in the first place?
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5$\begingroup$ You must distinguish between the clocks of a distant observer and the clocks of observers falling in with the contracting matter. The former sees the gravitational redshift, the latter sees nothing unusual at all. $\endgroup$– MichaelCommented May 2, 2013 at 14:45
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1$\begingroup$ Related question physics.stackexchange.com/q/21319 $\endgroup$– twistor59Commented May 2, 2013 at 15:23
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$\begingroup$ Also related: physics.stackexchange.com/q/48086 $\endgroup$– dmckee --- ex-moderator kittenCommented May 2, 2013 at 17:09
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$\begingroup$ That is of course true. Only I don't care much about others clocks but my own one. So it still stands as the question. From my and (hopefully) your frame of reference that contraction never reaches Rs. So why bother? $\endgroup$– luisCommented May 2, 2013 at 18:27
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$\begingroup$ Apart from that it holds even true from any! distance to Rs because time delay is INFINITE at Rs and for any other R>Rs it is finite. $\endgroup$– luisCommented May 2, 2013 at 18:50
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"Clocks stop" or "time stops" at the Schwarzschild radius only as seen by a far away observer. Where the matter is falling in, if it were wearing a wristwatch, it'd still see one second go by every second. Time continues as normal, and matter squeezes into the BH.
True, as seen by a far away observer, the matter will appear to shrink down to the Schwarzschild radius but slower and slower, all manner of light or other particles decreasing in energy (longer wavelengths, redshift) but this appearance may be remedied easily: just go dive into that BH and see for yourself that time doesn't stop!
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$\begingroup$ Of course time doesn't stop in relation to itself. I never told so. It stops for anyone who has any distance from Rs if matter has contracted to its Rs. $\endgroup$– luisCommented May 3, 2013 at 13:32
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$\begingroup$ Whatever the point of view from a co-moving observer of the contracting matter. From our frame of reference and any other position away from the contracting matter that object will never reach its Rs. No singularity has ever formed in our Universe and none will ever do so. What is happening from the perspective of some body which clocks freeze is a quite philosophical question. He is in "suspended animation" like some cartoon character only he will never find out if the object doesn't evaporate. $\endgroup$– luisCommented May 3, 2013 at 13:52
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$\begingroup$ Time doesn't stop neither at no point because no object ever reaches its Rs so there is no point where time dilation gets infinite. It is mathematically possible to move towards a point without ever reaching it. like for any second which passes you move 1/2 of the distance to the point. You will never reach it but always stay in motion! $\endgroup$– luisCommented May 3, 2013 at 14:26
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$\begingroup$ OK LET MAKE IT SIMPLER. Lets say a star had a gravitational collapse 10years ago at lets say 2ly distance. coordinate systems can be freely translated from one frame of reference to another (I hope we agree on this one). Now you say for the in-falling matter would reach Rs from that point T(10years ago)+Tm right? Now translate me Tm into Te (where Te would be some time coordinate in our earthly time). $\endgroup$– luisCommented May 3, 2013 at 14:58