Perhaps this only occurs within the event horizon of a black hole. Since the black hole is cut off from the rest of the universe, what happens inside cannot be observed.

: I know that strong gravitational fields, curve spacetime, hence slowing down light according to the uncurved spacetime. : Wouldn't it be possible to curve space-time in the opposite direction, so that light travelling in this region will travel faster according to an observer in an uncurved space-time frame. : This could mean that a space-ship travelling in this curved region could travel faster than light according to an observer in the uncurved region, but be travelling at less than c in it's curved space reference frame. : Does this mean that faster than light travel is possible without breaking the law which says that nothing can travel faster than the speed of light.