Time dilation near a black hole, with its extreme gravitational field, is intensified until time at the event horizon appears to be stopped completely. That is why black holes have also been referred to as 'frozen stars'. Matter falling toward the even horizon would appear to become redder and dimmer, but would not appear to ever completely fall into the hole.
Even as the Universe ages infinitely for us, however, an observer surviving the fall into a black hole would experience a 'normal' passage of time.
Answered by: Paul Walorski, B.A., Part-time Physics/Astronomy Instructor
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'Physicists like to think that all you have to do is say, these are the conditions, now what happens next?'
Richard Phillips Feynman