This is completely consistent with my statement :) Our time perception of the object remains the same, but the processes experienced by the object itself are m

This is completely consistent with my statement :) Our time perception of the object remains the same, but the processes experienced by the object itself are much slower, relative to how we perceive them. Specifically, if the object falling in is emitting blue light, and let's say that the frequency of blue light is one per second for the sake of doing some arithmetic, then that object keeps emitting 1/second and looks blue to itself. But in our frame of reference, those 1/second actually become .1/second (its time is moving slower then our time), and appears red.