This whole question and subquestions are based on the assumption that light rays on the event horizon are normal to the event horizon, so my apologies if this is not correct
In A Brief History of Time, in the frist one or two pages of chapter 7, "Black holes ain't so black", Hawking states the following fact: the paths of light rays on the event horizon could never approach one another.
He concludes that if they did, they had to run into each other sometime and thus they could (or have to?) fall into the black hole, thus they could not have been on the event horizon in the first place per the definition of an event horizon.
So he states that light rays on the event horizon have to run in parallel or away from each other as not to run into each other.
I have a few problems in understanding this:
- What does it mean for two light rays to run in parallel on an event horizon? (And what does it mean for two light rays to run away from each other)
I thought that light rays the event horizon was like a sphere, so a light ray on the event horizon would have to be a normal to this sphere as not to be falling into the black hole. Would this mean that the light stays stationary on the event horizon? This can't be true since the speed of light is a universal constant. I think the curving of spacetime comes in here, but I don't know how.
And: Would two parallel light rays on the event horizon be two normals at different positions on the event horizon (sphere)?
- Why do two light rays fall into the black hole if they run into each other?
If my assumption about parallel light rays being normals to the event horizon is correct, then I guess that non-parellel light rays would fall into the black hole because not all of the speed (c) of at least one of the light rays is pointed in the outward/normal direction, so gravity is stronger than this outward direction speed vector, so a ray falls into the black hole. But that would also happen if there was just one light ray not running into another light ray that was not a normal to the event horizon, right?
I've already read this question: What does Hawking mean by “Light rays that form the edge of the event horizon could never approach one another”?, but I did not understand the explanation in terms of null congruences