Well, I'm in a way, not qualified to ask this question as I've just started physics and presently learning Newtonian mechanics. Still I'm asking this out of curiosity, but quite serious as I am greatly wondered on how is it possible that there can be no speeds greater than light and all that stuff. So pardon me if my question is to naive or something like that.
Now consider this set up. We are in empty space and in a way isolated from all other interactions other than the interactions between the two masses which are present here. One of them is very, very massive and the other relatively light (may be the massive one is a very massive star or hypothetical object with a very, very high mass). Also suppose that they are very,very far, so that they don't collide soon enough (I've not numerically analysed the situation as I don't have enough knowledge for that )
Now both would attract each other due to gravitational force between them and they would accelerate them as they approach each other ( there would be also other forces acting like EM forces, but I'm neglecting them and assuming that there is no overall charge to cause significant force ).
Now what I think is that the lighter mass(as it will have a large acceleration owing to a tremendous force between them) can exceed the speed of light if they are far enough and the other one is massive enough, can't it?
In this situation I've ignored the time as I don't think it would matter if the time scale of this to take place is extremely large because it is a hypothetical experiment.
I just want to ask you that is my opinion wrong (that definitely is!)and how it is wrong. I'm not expecting you to tell the very precise reasoning behind your reply because I may not be able to digest it now or understand it completely (still it would be kind of you if you could explain me all that intuitively in simple words).
I'm looking forward for your replies.
The questions you mentioned doesn't takes into account exactly what I've asked. Also at this stage I don't want and mathematical treatment of relativity as I'm not in a position to understand it and asked this question out of curiosity . I'm quite satisfied with the answer by BowlOfRed and would brush up the concepts like escape velocity and things like that as now I feel I don't have the desired understanding of these concepts. Thanks for providing me links as they might be useful later. Thank You.