If black holes have mass but no size, does that imply zero uncertainty in position? If so, what does that imply for uncertainty in momentum?
Answer
General relativity is a classical theory. The Heisenberg uncertainty principle does not apply to it.
The research frontier in physics now exists in quantizing gravity and unifying it with the other three forces (strong , weak, electromagnetic). Once that is done the solution for the black hole will become a probability distribution and the Heisenberg principle will apply. The macroscopic classical solution of a point singularity will become a quantum mechanical uncertainty locus which will not change the macroscopic description. h_bar is a very small number and is already easily satisfied by the classical mechanics solutions all our constructions and engineering depend on.
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