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The answer is not exactly, but we can make a very good approximation. We currently have no quantum theory of gravity, but we do for the other fundamental interactions, so to explain black holes we use the quantum theories of these three, but use Einstein's General Relativity (a CLASSICAL theory) to account for gravity...this is OK because the quantum gravity effects only take place on very very small scales, namely the Planck lenght 10^-35m
At any instant the energy of the black hole is given by E=mc^2. A rather crude approximation is to equate the derivative of this to the Stefan-Boltzmann law, and after a little integration we get the result that for a black hole the same mass as our Sun it would take 10^66 years to completely evapourate.
So the answer to your question is a VERY small rate of energy loss, however the amazing result is that there is an "evapouration" of black holes.
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