Are they significantly different from the way that I know that Harry Potter is a wizard?

Don't get me wrong, I'm interested in hearing about some maximally elegant mathematical model which is consistent with the observations and the laws of physics on our side of the horizon. I just don't think I would then proceed to believe that what they described was a reality on the other side of that horizon.

I understand why you say this but it sounds awfully pessimistic. Its still an area of active theoretical research, we really don't know that there is no way to get information from a black hole, as I understand it from the black hole information paradox[1].

1. https://en.wikipedia.org/wiki/Black_hole_information_paradox

It wasn't supposed to be pessimistic. I think it would be kind of disappointing if there was a way to peek under the rug and see what's going on in there. Whatever we see is unlikely to be as fantastic as the idea that there are literally holes in the universe--holes which can be traversed, but only in one direction.

You can also see them as light bubbles: https://www.youtube.com/watch?v=uuWvJXZT5vQ

>I just don't think I would then proceed to believe that what they described was a reality on the other side of that horizon.

Does the physicist believe that? If we get past popular culture which mangles modern science, the physicists are throwing around lots of random "what if" ideas and seeing where they go. If one is good, their idea is popular enough other physicists spend time thinking about if. If one gets lucky, then someone comes up with a way to test the theory (using the layman version of theory). If one gets REALLY lucky, the test doesn't lead to it being rejected.

Sometimes there an be a long gap between when a physicist first thinks of a theory and someone finds a way to test it. Some ideas are still untestable, but may be interesting enough that physicists will still try to dive deeper and see where the idea goes.

But do they believe it is the truth? While some might, I think most keep a sort "what if, maybe" vibe, even on the theories they spend time looking into. They are invested, but that doesn't mean the believe it is the truth, only that it is the model worth spending their time investigating.

One key idea to consider, science does not give truth, it gives the model that best fits all known data without any claim to if that model is true or false.

But to know via scientific method requires proof (or disproof) by experimentation

Technically speaking there can be "disproof" but there is never "proof".

We have theories and experiments.

An experiment giving a result not in accord with the theory is an immediate disproof.

An experiment giving a result in accord with the theory is a confirmation possibly waiting for another experiment resulting in a disproof.

Proof exist only in mathematics.

You can get knowledge (e.g. mathematical) without observation. You can't get information without observation.