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I was trying to find an answer as to why light does not escape black holes and I stumbled upon this Phys.SE question. In the answer it said that:

"Since all future lies within the event horizon, photons are trapped inside the black hole."

But what does that mean? It sounds to me that if light were to escape a black hole it has to travel back in time. And this leads to another question, why does the future lie within the event horizon? This could make sense to me if there was another reason as to why light can't escape a black hole once it has passed through the event horizon, and as a result of that, the future lies within the event horizon. But that just makes the answer to the linked question a circular proof, it is the same as saying that light can not escape a black hole because of X reason and that is the reason why the future lies within the event horizon. And the future lies within the event horizon because of X reason. So is there an "X" reason, if so, what is it?

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Short answer: a) nothing inside the event horizon of a black hole can escape because b) the future of any event inside the event horizon is entirely within the event horizon because c) the gravity of the black hole has curved spacetime so much that the future points "in". In other words (c) implies (b) implies (a). Gravity is the reason you are looking for. –  Michael Brown Aug 20 '13 at 6:57
    
@MichaelBrown Is b) related to en.wikipedia.org/wiki/Light_cone where it says that "Events which lie neither in the past or future light cone of E cannot influence or be influenced by E in relativity."? –  Reds Aug 20 '13 at 7:12
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Yes, that's right. The light cone dictates the causal structure of spacetime, i.e. what events can affect what other events. In order for something to escape a black hole it would have to escape the light cone, i.e. violate causality. –  Michael Brown Aug 20 '13 at 7:15
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In this article, you may see an explicative image –  Trimok Aug 20 '13 at 7:52
    
@Trimok That article was really nice and informative, thank you. –  Reds Aug 20 '13 at 14:48

1 Answer 1

See my answer to Why is a black hole black? for a discussion of why light can't escape from a black hole.

The future light cone is simply the set of all spacetime points that can be reached from your starting position i.e. the edges of the cone are all the points you could reach travelling at the speed of light. So the statement that the future light cone lies within the event horizon is just a restatement of the fact that there is no way to get out through the event horizon without travelling faster than light. You're correct that this statement does not constitiute a proof. The answer I've linked above does constitute a proof, though it does require a bit of maths.

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