Foreword.
Since light can't escape from a black hole, we can assume that light is influenced by gravity.
So I can imagine that light that would otherwise escape from a black hole is in fact restrained/slowed from the gravity in the black hole.
A light ray/photon that is going in direction of a black hole can also be accelerated from black hole gravity? In this case is light going faster that light speed?
Argue each point if i'm wrong.
A black hole is a construct in General Relativity. In GR light follows geodesics with velocity c, these geodesics are very distorted close to the black hole:
The five geodesics drawn on the embedding surface of space-time outside the black hole represent the possible trajectories of a free-falling body passing at different distances from the black hole. The geodesics 1,2 and 3 are increasingly affected by the curvature. Geodesic 4 falls into the gravity well and intersects itself as it comes out. Geodesic 5 falls straight into the hole and is trapped.
In the case of a photon it has energy, and it follows the geodesic with c velocity, which cannot increase due to the theory of GR. Its energy ( frequency) can increase and this is what happens.
