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

We study quantum corrections for the Schwarzshild black hole by considering it as a vacuum solution of a two-dimensional (2D) dilaton gravity theory obtained by spherical reduction of 4D gravity coupled with matter. We find perturbatively the vacuum solution for the standard one-loop effective action in the case of null-dust matter and in the case of minimally coupled scalar field. The corresponding state is in both cases a 2D Hartle-Hawking vacuum, and we evaluate the corresponding quantum corrections for the thermodynamic parameters of the black hole. We also find that the standard effective action does not allow boundary conditions corresponding to a 4D Hartle-Hawking vacuum state.