Picture a light wave orthogonal to and just above the event horizon of a black hole, fired directly away from the black hole.
If the black hole is of sufficient mass, the light would be pulled back towards the black hole and would eventually reverse directions.
My two questions are:
If the black hole is of sufficient mass, the light would be pulled back towards the black hole
If the light was emitted from outside the event horizon, then the black hole is necessarily not of sufficient mass. Once the photon is emitted, it moves at the local speed of light. It is too late to add mass to the black hole to change its trajectory. The light when it is far from the black hole will be observed to have less energy than an observer at the event would have seen.
the light would be pulled back towards the black hole and would eventually reverse directions.
No, the light never "reverses" directions the way a ball might when thrown upward. Spacetime near the black hole (inside the event horizon) is sufficiently curved that all directions point into the black hole. There is no direction that you can point the light that leads to outside.
No, your assumption is wrong.
All vanilla black holes (no charge, no spin) have an event horizon. If you are outside the event horizon, you are far enough away that light pointed directly away can escape to infinity. As in all gravitational wells, it will be red shifted. The light that reaches infinity will be less energetic that it would have been without the gravitational well. Light emitted very close to the event horizon is strongly red shifted.
Time passes slowly in a gravitational well. The deeper in, the more slowly. So it takes longer to escape than you might expect.
Inside the event horizon, everything, light included, travels on a trajectory that ends at the singularity.
Outside the black hole, there is a direction perpendicular to the event horizon toward the outside. An excited atom that decays can send a photon in that direction. It will travel infinitely far away. Photons sent in other directions travel on "straight" geodesics. But in curved space, "straight" bends toward the event horizon. The trajectory may well pass through the event horizon and end on the singularity.
However, if the excited atom falls past the event horizon, all directions lead to the singularity. Light pointed in what would have been the outward direction does not travel outward. Inside the event horizon, space is curved enough that intuition is not helpful. Perhaps you might think of the photon swimming upstream, but not fast enough. But of course there are problems with that thought.
Exactly at the event horizon, light would never go anywhere. Of course, you can't put light exactly at a point. It would either be a little inside and get sucked in. Or a little outside and an extremely red shifted remnant would escape.
