  The one-loop quantum corrections for BTZ black hole are considered using the
dimensionally reduced 2D model. Cases of 3D minimal and conformal coupling are
analyzed. Two cases are considered: minimally coupled and conformally coupled
3D scalar matter. In the minimal case, the Hartle-Hawking and Unruh vacuum
states are defined and the corresponding semiclassical corrections of the
geometry are found. The calculations are done for the conformal case too, in
order to make the comparison with the exact results obtained previously in the
special case of spinless black hole. Beside that we find exact corrections for
AdS black hole for 2D minimally coupled scalar field in the Hatrle-Hawking and
Boulware state
