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What happens if the ‘Hawking radiation’ theory is incorrect, and it doesn’t evaporate?

We're in big trouble, but not because of the micro black hole.

This is rooted in the basics of quantum mechanics, and if that 'quits working' then the sun will go out and a host of other bad things will happen. The problem in detecting Hawking radiation is not that the theory is shaky, but that the conditions to detect it are hard to come by. You need a black hole, for starters, and close enough that you can detect the Hawking radiation - which ends up looking like photons, and so gets lost in lots and lots of other photons between us and the nearest black holes we can detect (by observing effects on other bodies, of course).

I think the problem is just the opposite - at the highest energy states they can reach with the LHC, any black hole will evaporate so fast we won't even know it was there.