The speed of light is a constant. It can slow down travelling through a medium but gravity is not a medium, it is a warp in spacetime. Gravitational pull can bend light but that does not mean light slows down. I believe someone else made a prior post that passing through a gravity field does not slow anything down. The net momentum is preserved. I'm not sure if I posited this correctly, but that was my understanding. In fact, for massive objects gravity may well be used for a sling shot effect, actually using gravity to speed up an object, except light of course. Black Holes may be different, but the lensing effect (caused by gravity) does not interfere with the speed of light, IMO..