I think the extreme time dilation at Miller's planet is due to being so close to the black hole (you must be very
close to the event horizon for the time dilation to be that significant), and not so much a property of the planet itself. But at any rate, if you were to look at the planet from far away, what would it look like?
Actually, you wouldn't see much of anything! Just the dark abyss of the black hole. The reason is because gravitational time dilation goes hand in hand with gravitational redshift (the light gets stretched as it climbs out of the gravitational well), and for one hour to be dilated to 7 years corresponds to the light being stretched by a factor of over 61000. This would turn visible light into microwaves (centimeter wavelengths), and the light would also be dimmed by the same factor.
So to your eye you would just see darkness, but perhaps a very
sensitive microwave telescope could pick out the radiation, in which case you would indeed observe the planet and everything on it evolving very slowly.
Source of the post
The same applies to the ship traveling around Gargantua, when they say that slingshot maneuver would cost them 51 plus Earth-years. If a perpendicular observer (outside the time-shift) could see the entire movement, what would be the outcome for him? Would he see the ship fast approaching the black hole and then "slowing down" (or even "disappearing"??) and then coming out in the other side only 51 years after??
Basically, yeah. Their clocks slowing down with respect to yours would again correspond to their light being reddened and dimmed to invisibility. It would seem as if they just vanished near the event horizon, but then if you waited around for another 51 years you would see them emerge, since they didn't actually cross it, but passed very close to it.
I know right?
Relativity is one of the weirder, counter-intuitive, and seemingly fantasy parts of physics. But it's totally a real thing and it applies everywhere, not just near black holes or close to the speed of light. If you are near sea level, time for you passes more slowly than it does for someone who is at higher elevation, because the gravitational field is stronger for you. Time passes about 10 nanoseconds per day more quickly with every 1000m elevation that you gain, and this is actually measurable!