Appears in collection : Damour Fest: Adventures in Gravitation

In this talk, I will discuss whether the black hole metric remains to be a solution of gravitational equations provided the classical gravitational action is modified by the generally non-local terms after integrating out the quantum matter. The story appears to be dramatically different for the Hartle-Hawking state and for the Boulware state. The discussion will be based on the analysis of the 2d RST model and the 4d theory with a CFT as the quantum matter.