Paradoxes that have come up for special relativity

[AVNguyen]

The problem here is that the tunnel is rotating: the rock will hit the side after a certain amount of time. (right?)

To my sollution,yes, it's right.However, that's not my point.
My point is what's happened to a matter in a gravitational field without contact with anything. Assume that the space it's vacuum and rotating.Will it become an endless satelite or it has to stop at the centre of the gravitational field.That's why I also included the black hole in my last thread so you will not make so much assumption like sa wanted to classified.
I just want to discuss this "classic thought experiment" in modern physics situation.That's all.I have to say that I am also not sure about the sollution for this.So maybe we can find something in common after having discussion.

 

[Garth]

The standard solution to the problem of a mass freely faling down a tube through the earth, neglecting air resistance and friction against the side of the tube, is the mass will oscillate from one side to the other, coming to rest as it reaches the surface before descending again, at a frequency equal to the circular orbital period of a satellite at zero altitude (in vacuo), no matter if the tube goes through the centre of the Earth, or is a chord parallel to such.

Garth

 

[AVNguyen]

Maybe I have to explain my paradox a little bit more.
According to RT, or GR to be exact, matters will be dragged in a black hole. During the period, that matter will accelarate like the stone which is dragged into the centre of the Earth. Clearly what has happened to the stone in the Earth situation as you all say, but what's happened to the black hole's model.Will that stone travel restlessly? will it reach the other surface of the black hole?( I think we can assume we have one) or it will have to stop at the singularity inside the centre of the black hole.
hope you understand what i mean

 

[gonzo]

I was under the impression that with a black hole the large mass bends space in such a way that "all roads lead to Rome", Rome being the center of the the black hole. So, once inside the event horizon, any direction an object moves is always towards the center. Or have I misunderstood something about black holes?

 

[selfAdjoint]

Certainly in a Schwarzschild metric the radial direction becomes timelike inside the horizon, which means falling inward toward the center is as ineluctible as the passage of time.