What's the relevance of this? I don't even know whether I should agree with "there is a finite time after which there is no source of those photons" or not. As presented, that statement is too vague and ill-defined to even discuss in the context of GR.If you both agree that photons will continue to be received by the outside observer indefinitely then it does not follow that there is a finite time after which there is no source of those photons.

I've always been specific about what I was claiming: the point where the in-falling observer crosses the event horizon drops out of the outside observer's future light cone after a finite time. Even with that settled, your statement doesn't make sense: let

*X*= "light emitted by the in-falling observer will continue to be received by the outside observer indefinitely"

*Y*= "the in-falling observer becomes irretrievable to the outside observer in a finite time on the outside observer's clock".

*X*, and it doesn't follow that

*Y*", then read literally you're saying "

*X*doesn't imply

*Y*". Now that's true, but irrelevant: nobody is trying to argue that

*Y*is true *because*

*X*is. I'm claiming that

*Y*is true, independently of

*X*, because I've depicted the situation on a Kruskal chart.

That's obvious, so I think it's more likely you meant "

*X*implies

*Y*is false". And that simply isn't true.

*X*and

*Y*together mean that the horizon crossing event falls out of the outside observer's

*future*light cone after a finite time, but never falls into his

*past*light cone. There's really no reason

*X*should invalidate

*Y*. Both are visible on the Kruskal diagram for instance.

Why not? What's happening is simply that light emitted by the in-falling observer has a progressively harder time climbing out of the black hole's gravitational well and reaching the outside observer. Another point of view is that the outside observer is accelerating away from the light, which is how the situation appears on a Kruskal diagram. He'd get all the light in a finite time if he simply allowed himself to free-fall past the event horizon.There cannot be some sort of "infinite cache" of light waiting to make its journey to the outside observer

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