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Just a silly question. If black holes evatorate completely due to Hawking radiation, how can the area theorem hold if no black hole is left at the end? If no black hole, no area. How is compensated the event horizon area increasing with the accepted emission of hawking radiation making the black hole less massive, and so becoming smaller and smaller!

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Thus, the laws of black-hole thermodynamics only hold good in classical GR: thus, the area theorem only states that classical effects cannot decrease the area of the event horizon. When one considers effects from quantum field theory such as Hawking Radiation, the area theorem fails to apply.

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The area theorem makes use of the Raychaudhuri equation for a congruence of null geodesics together with the null energy condition, but exotic fields can violate this law.

Indeed the Hawking radiation stress energy tensor doesn’t satisfy the null energy condition, therefore the second law is violated and the black hole can lose mass and shrink.

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