That's not science, that's making assertions and yelling 'fallacy!' at other people
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Yes, that's exactly what using one of the outputs of a theory to claim it is unfalsifiable is like.
We know that General Relativity breaks at the singularity which means the maths are wrong there, but to replace GR you have to: 1) solve the BH thingy and 2) be compatible with GR in the other scenarios. GR is not a "hypothesis", it's well established fact and has been verified to death. While we wait a more general theoretical model comes out (string theory? quantum loop gravity? who knows), working with the imperfect tools we have is the most sensible approach.
I mean we haven’t reconciled quantum & GR yet but we still use quantum for quantum scale things and GR for larger scale distances just fine. It’s not impossible to have a separate model for within the singularity that only applies within the singularity without having to unify it with GR. As long as there are falsifiable claims being made within the context of the new theory that can be tested somehow, that’s all that matters.
I'm not sure I follow when you say "it's not impossible". I would rephrase that as "it's useful", as is it's productive to work with the tools we have.
But in the end we all know that new physics need to be developed because the assumption is that there is only one reality and thus we should strive to reach a unifying theoretical model. Or are you suggesting there it is not possible to achieve a single theoretical model of reality?
Well, the thing I was originally suggesting was that people should not be so quick to call something unfalsifiable just because GR predicts we can't directly look inside black holes.