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Agreed there is a void in clarification, as I had issues with this before, but there would be enough time for this to occur because it would happen pretty far away from the singularity. It's once you get close to that, that time appears to slow. Tidal Forces happen quite far away from the singularity and the majority of warped space.
If this imaginary astronaut is falling feet first towards a black hole, his feet are closer to the center of the black hole than his head. The force of gravity is therefore stronger on his feet than on his head. The difference in pull creates what is called a tidal force. This makes the astronaut (or anything else that gets too close) stretch out long and thin. The difference in time would actually have no effect. You have to remember that time frames stay to their own, anything outside of the frame is different from things outside of the frame. To the feet, they feel super acceleration toward the singularity and watch as the head takes longer and longer to accelerate, and time appears to remain the same. To the head, the feet appear to super accelerate toward the singularity and it takes longer for the head to catch up, while time appears to remain the same because both frames of reference witness the same effect.
Yes the time is different, but the effect remains the same.
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