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The diagram is necessarily correct (it shows a valid solution to the EFE), and I think so is Genady’s interpretation of it. The thing is that, at the event horizon, something very unintuitive happens - the physical meaning of the coordinates we use is no longer the way we are accustomed to. Imagine an astronaut in free fall, just as he crosses the horizon - let’s for simplicity’s sake say his feet emit light. Once his feet have crossed the horizon, and always assuming free fall, this light signal is now no longer “below” the eyes, but in their future. Light below the horizon is perfectly free to propagate in all spatial directions, yet it can still never leave the BH, because the singularity is in the future, and the horizon is in the past. It is no longer a question of up, down, above or below, once you’re past the horizon. Thus, for the astronaut, the light leaves his feet, and his eyes will necessarily “meet” it, because he’s in free fall. Both age towards the singularity, their relative velocity remains c (so everything is locally Minkowskian), yet their geodesics must intersect, just as the diagram shows. Thus he sees his feet like normal, perhaps slightly redshifted and dimmed. He will otherwise never notice anything special at the horizon. And he can’t, because locally everything must look Minkowskian. This is probably the biggest mistake people make when trying to visualise black holes - they think that, past the horizon, the singularity is “down”; but it’s not, it’s in the future. Likewise, the horizon isn’t “up”, but in the past. This is extremely important to understand, or else there’ll be all sorts of misunderstandings. It’s the other way around, see also above - light past the horizon remains past the horizon, but the eyes which see that light are falling inwards, and can intersect that light in the future.

The primed observer, falling through the horizon at event C', sees the unprimed observer, which is falling through the horizon at event C.