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We study quantum corrections for the Schwarzshild black hole by consideringit as a vacuum solution of a 2D dilaton gravity theory obtained by sphericalreduction of 4D gravity coupled with matter. We find perturbatively the vacuumsolution for the standard one-loop effective action in the case of null-dustmatter and in the case of minimally coupled scalar field. The correspondingstate is in both cases 2D Hartle-Hawking vacuum, and we evaluate thecorresponding quantum corrections for the thermodynamical parameters of theblack hole. We also find that the standard effective action does not allowboundary conditions corresponding to a 4D Hartle-Hawking vacuum state.Comment: 19 pages, Latex, some corrections are made in Sect.

One-loop corrections for a Schwarzschild black hole via 2D dilaton gravity