Do black holes cause gravitational redshift? Suppose a light ray is emitted by a light source very close to the black hole's singularity away from the black hole's gravitational center. Why won't the light escape? Shouldn't the massive gravity of the black hole just cause massive redshift in the light ray? How does it pull it back? I know there might be many questions similar to this but I just need a basic answer for the redshift part. I understand that if a light ray is passing nearby the black hole, then it bends and gets pulled inside. But what if the light is going perpendicularly away from the black hole? The source is inside the event horizon of course. Otherwise this is just a normal case.
 A: It is not so simple. On your question I think you try to estimate its behavior based on the Newtonian Mechanics. But this goes based on integrated curves based on the Einstein Field Equations and its mathematics is totally different. For example, the orbits aren't are generally not closed and not stable.
If the light will go away from the black hole, it will redshift, but will be able to go away. Light passing the event horizon, will go into the hole and will never get out.
Light going initially on a circular orbit will also end in the black hole if it started below $3/2R_g$.
You can read more about the stable/metastable and unstable orbits around the BH here.
A: The radial coordinate inside the black hole is time-like, so when you are into the black hole (according to standard General Relativity and considering a Schwarzschild black hole) you are forced to go to the singularity. It's like if the radial coordinate is our usual time coordinate, in which you can't travel to the past.

See for example this Kruskal diagram of the black hole. The maximum speed you can reach is $ c $, that means going on a $ 45° $ line into the diagram. Massive particles are forced to stay into the light cone and they follow $ 0-45° $ trajectories. You can't do better than $ 45° $ and you can't go away from singularity.
Moreover, the horizon is the infinite redshift surface (more precisely,  the effective infinite redshift surface is slightly outside the horizon, because you don't have an experimental device with infinite sensibility).
