Black hole entropy and the semiclassical approximation

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We compute the entropy of the Hawking radiation for an evaporating black hole, in 1+1 dimensions and in 3+1 dimensions. We investigate the validity of the semiclassical approximation for the evaporation process. It appears that there might be a large entropy of entanglement between the classical degrees of freedom describing the black hole and the radiation fields when the theory of quantum gravity plus matter is considered.
9 pages, 1 figure (included), plain tex. (Section on quantum gravity is rewritten to explain basic ideas more clearly.)

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