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How does Hawking radiation help in information conservation? Doesn't it create a paradox, as the particle-antiparticle pair created at the event horizon has nothing to do with the matter that has already fallen into the black hole thousands of years ago? How does it prove that information is not being destroyed by black holes?

Can it be that black holes are five or six-dimensional objects and hence cannot be fully explained by our four-dimensional understanding of this universe? Because our 4D physics breaks down at the singularity. I apologize for the mistakes I may have made, I am no physicist, I am a high schooler and asked this out of curiosity.

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    $\begingroup$ “Doesn't [the Hawking radiation] create a paradox … ?” - The loss of information is not the same as the information paradox. Information can be lost with no problem. A well known example is that a black hole made of antimatter is the same as one made of matter. So the information of matter vs. antimatter is lost and - no one cares. No paradox. However, if the black hole evaporates, then two different external observers would see different outcomes, which is impossible. The paradox is not with the loss of information per se, but with the reality contradicting itself, if black holes evaporate. $\endgroup$
    – safesphere
    Commented Mar 25 at 0:05

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This is known as the black hole information loss paradox. You are correct in stating that (at least at a first glance) the Hawking radiation is not correlated to the matter that has fallen into the black hole, apart from a handful of properties: the mass, electric charge, and spin of the black hole do influence the radiation.

If one trusts Hawking's calculation completely (i.e., until the very end of the black hole evaporation process), then information seems to be lost. This is meant in the sense that if you only have a ``screenshot'' of the universe at a time after the black hole has evaporated you cannot compute what happened before the black hole was created. The information at late times does not contain all of the information at early times.

Many physicists believe this is a clue that something is wrong in our understanding of gravity or quantum mechanics. There are many proposed solutions to the paradox, but I don't know of any that consist of using five or six-dimensional physics. Many of them do use different mechanisms to get rid of the singularity, though.

I always like to mention that it is not a consensus that the black hole information paradox is a problem. There are important people working in general relativity (and more specifically in something we call quantum field theory in curved spacetime, which is the framework in which Hawking radiation is computed) that believe there is nothing wrong with the loss of information, and that it is actually a feature rather than a bug. Two notable examples of scientists with this point of view are William Unruh and Robert Wald.

In summary, you have posed a very good question. So good that many experienced physicists work precisely with the goal of trying to answer it. There is no way of providing a closed answer to your question yet because no one really knows what happens. Maybe information is lost, maybe it isn't. We don't know yet.

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