Does time pass faster or slower close to the black hole?
According to Einstein's General Theory of Relativity, time passes more slowly (as seen by
an outside observer) in a gravitational field. The stronger the gravitational field, the greater the time dilation effect. This has been verified on Earth by accurately measuring the passage of time at the top and bottom of a tall building. Because gravity weakens as distance from the Earth's center increases, the readings of extremely accurate atomic clocks that are synchronized at sea level diverge if one is raised to the top of the structure.
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.
Paul Walorski, B.A., Part-time Physics/Astronomy Instructor