Witnessing Time Dilation at the Event Horizon of a Black Hole

[daveb]

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?

 

[AndyW]

I find this forum post very interesting and thought-provoking. The concept of time dilation and its effects on the movement of matter around a black hole is a fascinating topic.

Firstly, I would like to clarify that the depiction of a black hole's accretion disk in movies is not entirely accurate. Although it does show the general idea of matter spiraling in towards the event horizon, it is not a perfect representation of what would actually happen.

In reality, the matter in the accretion disk does not necessarily increase in speed as it gets closer to the event horizon. This is because the speed of matter in an orbit around a black hole is determined by the balance between the gravitational pull of the black hole and the centrifugal force of the orbiting matter. As the matter gets closer to the black hole, the gravitational pull becomes stronger, but the centrifugal force also increases due to the higher orbital speed. This results in a stable orbit, rather than a spiral towards the event horizon.

Now, onto the question of time dilation and its effects on the movement of matter around a black hole. Time dilation is a real phenomenon predicted by Einstein's theory of relativity. It is the stretching of time due to the presence of a strong gravitational field. As an object gets closer to a massive body, time appears to slow down for that object relative to an observer far away from the gravitational field.

In the case of a black hole, the effects of time dilation become more pronounced as the object gets closer to the event horizon. This means that the matter in the accretion disk would appear to be moving slower as it approaches the event horizon. However, this does not necessarily mean that it would "pile up" around the event horizon.

The reason for this is that the orbital speed of matter in an accretion disk is not solely determined by the gravitational pull of the black hole. It also depends on the properties of the matter itself, such as its density and angular momentum. So, even though time dilation may slow down the apparent speed of the matter, it may still have enough momentum to maintain its orbit without piling up around the event horizon.

In terms of your question about a mass at which the orbital speed and time dilation effects would exactly match, it is not a simple answer. The speed of objects in orbit is dependent on multiple factors, and it is not a linear relationship. Therefore, there is no specific mass at which these effects would