The galaxy NGC4261 is believed to contain a black hole that weighs about one hundred thousand times as much as our sun, with a diameter the size of our solar system. (http://www.damtp.cam.ac.uk/user/gr/public/bh_obsv.html) Now, imagine that we clear the space around the black hole and use some kind of spaceship to first build up a near light speed velocity. Then, from a distance of a few "light days" (we suppose that this black hole has a diameter of almost a "light day") we aim straight at the black hole, turn off the engines and just plainly falls towards it. My question is; If the spaceship already is at very near light speed, why doesn't the massive gravitational field from the black hole manage to accelerate the spaceship to above light speed before it reaches the black hole? Any relativistic mass increase of the spaceship would not make any difference since it is accelerated by a gravitational field (and not by its engines), so what is stopping it?