The equivalence principle as I understand it goes something like this:
Let's suppose you're in a black box in the middle of nowhere in space, and we accelerate this black box in some direction. You'd feel a force just like you would if you were in a gravitational field which was causing the same acceleration. In fact there is no experiment that you can do to say for sure if you are in a gravitational field or just accelerating in some direction in a black box.
OK, so now let's imagine this elevator is being accelerated. Surely it can't accelerate at a constant rate forever, right? It's limited by the speed of light. So at some point or another the elevator will start to slow down. This sort of deceleration just does not happen in a gravitational field.
Where did I go wrong?