What is your opinion of the hawking radiation mechanism, does that actually lower the entropy of the black hole?
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The law of constant or increasing entropy holds for closed systems. – anna v Jan 26 '14 at 09:50
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It is not a matter of opinions, it may be calculated. The Hawking radiation inevitably shrinks primarily the black hole mass (it may also change the angular momentum and charges but they are being reduced "proportionally" to the mass in the limit of many Hawking quanta). Lighter black holes carry a smaller entropy.
The reduction of the black hole entropy doesn't contradict the second law of thermodynamics because the Hawking radiation which is newly created carries some entropy, too. In fact, the total entropy of (the black hole + the Hawking radiation) is continuing to increase.
Luboš Motl
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I'm upvoting this, but, in consequence, I have to mention that the fact that it can be calculated doesn't mean it's there: It's probably the most inherently unobservable phenomenon to be anywhere nearly as widely hypothesized in physics. – Edouard Feb 18 '20 at 19:00