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Hawking Radiation Energy and Entropy from a Bianchi-Smerlak Semiclassical Black Hole

Eugenio Bianchi and Matteo Smerlak have found a relationship between the Hawking radiation energy and von Neumann entropy in a conformal field emitted by a semiclassical two-dimensional black hole. We compare this relationship with what might be expected for unitary evolution of a quantum black hole in four and higher dimensions. If one neglects the expected increase in the radiation entropy over the decrease in the black hole Bekenstein-Hawking A/4 entropy that arises from the scattering of the radiation by the barrier near the black hole, the relation works very well, except near the peak of the radiation von Neumann entropy and near the final evaporation. These discrepancies are calculated and discussed as tiny differences between a semiclassical treatment and a quantum gravity treatment.