Accretion disks (1 Viewer)

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I got to thinking the other day while watching Superman Returns about the scene during the opening credits where it shows the accretion disk around a black hole. The scene showed an inward spiral of gas and other matter increasing speed as the matter approached the event horizon. Now, understanding that it was only a movie, I wondered what it would actually look like.
Objects orbit a more massive body faster if they are closer to that body. So, as matter spirals in towards the event horizon, it would pick up speed. At the edge of the horizon, it would be zipping around the edge (like water speeding down a drain). However, as it approached the event horizon, an observer would see the effects of time dilation, and the matter would appear to be moving slower. So, which one wins over? I would have to assume that time dilation wins over at all distances from the event horizon, so that no matter what, as matter approached the event horizon, it would appear to be moving slower in our frame of reference. This would mean the matter would appear to "pile up" around the event horizon, and you would see what appears to be a ring around the hole.
So, taking this, and the knowledge that for a normal star (such as our sun) the closer you get to the star the faster a body orbits it. Therefore, is there some mass at which as the orbit gets closer to the body, the effects of the faster orbital speed exactly matches the time dilation effect (because even the sun has one, albeit mostly unnoticeable), and the orbital speeds are identical regardless of distance?
 

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