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?

  • $\begingroup$ Showing that the Schwarzschild black hole will be emitting Hawking radiation at any given moment (using semi-classical gravity which is an approach to modeling quantum fields on curved spacetime, without treating the spacetime itself in a quantum way as would need to be done in a true theory of quantum gravity) is not the same as showing that its event horizon actually shrinks over time, I would think. $\endgroup$ – Hypnosifl Dec 5 '14 at 3:04
  • $\begingroup$ The Schwarzschild metric is static by definition. If the metric changes over time then it's not the Schwarzschild metric. Simple as that. $\endgroup$ – Jold Dec 5 '14 at 4:00

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).

  • 2
    $\begingroup$ Doing a little searching, it seems that the spacetime of an evaporating black hole is often modeled in general relativity using a Vaidya metric but having it absorb negative mass/energy instead of positive, for example p. 4 of this paper says "In the dynamical horizon equation, if black hole absorbs negative energy, black hole radius decreases." $\endgroup$ – Hypnosifl Dec 5 '14 at 3:02

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