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I was recently playing around with classic Newtonian mechanics and calculated that the Earth would have to be compressed to a spherical region of $8.8 \ mm$ (Its Schwarzchild radius) to turn its surface escape velocity to the speed of light, i.e turn it into a blackhole. Is the event horizon only the region inside which its escape velocity would be equal to or greater than $c$? What happens to the mass inside this region? Is the mass roughly contained within the Schwarzchild radius or does any object compressed to its corresponding Schwarzchild radius have its mass compressed to a singularity? I hope the question has been clear enough.

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The answer is it depends on which observer we are talking about - an observer "with" the collapsing mass sees it and them crushed to a singularity; an external observer "sees" (though see below) the mass frozen just at the event horizon.

In GR and a standard black hole, there is only one future for a mass that finds itself at or inside the event horizon, and that is to move inwards towards the singularity. The maximum time that this would take (for a non-spinning black hole) is $4 GM/3c^3 = 7\times10^{-6} M/M_{\odot}$ seconds. i.e. not long for a stellar-mass black hole!

This can be a tricky concept - what I mean is that the mass is compelled to move inwards, there is no force or allowable motion that can change this.

However an even trickier concept is that the above is written from the point of view of an observer "riding" with the mass. External observers could witness the effects of gravitational time dilation. Light emitted from the material falling into the event horizon will become redshifted, because from the point of view of the external observer, its "clock" is running slow. Thus the collapse will appear to slow down and essentially freeze at the event horizon where the time dilation becomes infinite. In practice this cannot be seen because any light emitted would also be infinitely redshifted and so for all practical purposes, the mass has disappeared, and ceases to communicate with the rest of our universe.

See also

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

Watching something fall into a black hole from far away

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  • $\begingroup$ Looking back, it feels great to see how much more I understand your answer now. $\endgroup$ Jun 30, 2017 at 16:11

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