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I recently saw this question, and came across a claim from Anixx that a Schwarzschild black hole cannot evaporate because it is static:

@HDE 226868 Schwartzshield solution is a static one, which does not change with time.

Yet here there exists a detailed derivation of how a Schwarzschild black hole can emit Hawking radiation.

Is Wikipedia right? Can Schwarzschild black holes evaporate?

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I don't think the answer is too exciting. The Schwarzschild solution is a static solution to the Einstein field equations. The Einstein field equations alone don't take into account quantum effects. Taking quantum effects into account will give you a modification of the solution, and the result that the Schwarzschild 'solution' is no longer static (and so could hardly be called a 'solution' any more).