Speed of Objects Falling to Black Hole Center

[jBase]

I was wondering what is known about the speed of objects falling to the centre of a Black Hole?
If a number of identical objects, initially located outside the event horizon, were propelled at varying speeds towards a black hole, would that variability be maintained as they pass through the horizon and all the way to the centre, or would they all approach some limiting speed?
Inside the event horizon, could an object overtake another if it's initial speed was higher, yet because they were propelled at different times, it passed through the horizon after the other?

 

[Ibix]

I am no expert but I would think that the effect of gravity from the black hole would be constant acceleration, or close to constant.

Most definitely not. This isn't even true in Newtonian gravity - acceleration varies with distance.

I don't know whether it's possible to overtake inside an event horizon. Probably, since spacetime must be locally flat even inside a black hole. But I'll let more knowledgeable folk answer that one.

 

[PeterDonis]

If a number of identical objects, initially located outside the event horizon, were propelled at varying speeds towards a black hole, would that variability be maintained as they pass through the horizon and all the way to the centre

This question can't be answered as you ask it, because the concept of "speed" you are using no longer works inside the horizon. You are defining "speed", as far as I can tell, as "speed relative to an observer who is hovering at a constant altitude". But below the horizon, it is impossible for any observer to hover at a constant altitude. So "speed" defined this way doesn't make sense inside the horizon.

Inside the event horizon, could an object overtake another if it's initial speed was higher, yet because they were propelled at different times, it passed through the horizon after the other?

This question, however, can be answered, since both objects are launched from outside the horizon, where "initial speed" makes sense (we can just measure it relative to an observer hovering at the altitude from which both objects are launched). The answer is that overtaking is possible, if the second object's initial speed is fast enough compared to the first, and the time between launches (as measured by the hovering observer) is short enough. But there will be a limiting time between launches, after which, no matter how fast you launch the second object, it can't possibly overtake the first--even if the second "object" is actually a light ray (which is the fastest possible thing you could launch).