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Imagine that you, unfortunately, fell into a black hole. For external observers, you would slowly go closer and closer to the event horizon. Then, when you reach the event horizon, you would appear to be frozen there and get red-shifted for an external viewer.

Since it takes infinite amount of time to enter the event horizon, which will happen instantly for you. It is possible that by the time you enter, the black hole, or maybe even the universe, has ceased to exist. So, how would you enter it if it doesn't even exist anymore?

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Don't confuse what is happening locally by observations made externally. As you stated, to an external observer, the person falling in appears to take an infinite amount of time. However, what is happening locally (in the frame of the person falling in) is not what is happening according to an external observer.

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It is possible that by the time you enter, the black hole, or maybe even the universe, has ceased to exist

This assumes there exists some absolute time for the whole universe. This is exactly the notion that relativity has gotten rid off. So for us to be able to answer your question, we would need to know, what kind of time you mean when you say "by the time".

From your question, it seems you assume external observer's time (I am going to assume this means time in Schwarzchild coordinates) is the absolute one. Then the answer is simple, the external observer's notion of time breaks down at the event horizon. There is no continuation of his time below the event horizon. In fact, below the event horizon the coordinate he calls "time" becomes spatial, which shows the severity of the break down of the coordinate he calls time. And it makes sense as there is no way to compare clocks between observer under event horizon and one above it, so how could he meaningfully define time under event horizon at all?

Now, you can actually define some coordinates which cover whole spacetime (both below and above event horizon) with one coordinate being "The Time". But there is infinitely many of them and none is distinguished by physics itself (at least I never saw one), they are just some mathematical coordinates. And according to which one you pick, the picture of what is happening will differ.

In general relativity you should be careful which concepts you wish to look at from global point of view. Some concepts are meaningful only when viewed locally.

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