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By assuming simultaneously the unitarity of the Hawking evaporation and the universality of Bekenstein entropy bound as well as the validity of cosmic censorship conjecture, we find that the black hole evaporation rate could evolve from the usual inverse square law in black hole mass into a constant evaporation rate near the end of the Hawking evaporation before quantum gravity could come into play, inferring a slightly longer lifetime for lighter black holes.

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