my respect to this great community!
I've been thinking on the mechanics of a collapsing star and this led me to the following paradox which I can't explain:
Assume I live inside a perfect sphere (of non zero thickness) of matter. Newton showed that inside such a sphere observer feels no gravity, because in every interior point all gravity vectors add up to 0.
(I'm not sure if this holds in GR. I don't have the mathematical skill to verify it. But I assume it probably does.)
The basic assumption of SR is that the laws of physics work exactly the same for all observers in uniform motion. Living inside the spehere I feel no forces so I assume all laws of physics will work normally in my frame of reference.
Now the interesting part: Assume that the sphere is made of some incredibly dense and incredibly strong material (this assumption is not necessary - more on that later - but it will help to illustrate). Perhaps some degenerate quark matter held together by the Strong Force (not that important).
Consider what happens if we start to increase the density and mass of the sphere. As the mass increases I continue to live my happy life inside the sphere, as all gravity still cancells itself out.
But as some point the mass of the sphere is so great that it's Schwarzschild Radius becomes greater than the radius of the sphere. For the outside observers the sphere just became a Black Hole.
And now I live inside a Black Hole. Space and time switch places... The singularity is in my kitchen... But at no point during the mass increase process I saw anything happening at all. I wouldn't be able to measure in any experiment that the mass around me increased. And yet instantly I have this singularity in my kitchen. Impossible. It's not continous. Paradox.
What's the point of this? I speculate that the core of a collapsing star has the exact same experiance. It never notices that an event horizon emerged around it. That is also the reason why the assumption that the sphere is strong is irrelevant. I'm interested in the very short instant of time during the core collapse right before event horizon emerges.
I appreciate any insght you might have on how this paradox can be resolved.
