BLACK-HOLE ENTROPY - OFF-SHELL VERSUS ON SHELL

Different methods of calculation of quantum corrections to the thermod ynamical characteristics of a black hole are compared. The general rel ation between on-shell and off-shell approaches is discussed. We consi der the simplified 2D model with the dilaton gravity and show in its f ramework that the observable thermodynamical black hole entropy can be presented in the form S-TD=pi r(+)(-2)+S-SM-S-Rindler(SM). Here, (r) over bar(+) is the radius of the horizon shifted because of the quantu m back reaction effect, S-SM is the statistical-mechanical entropy, de termined as S-SM=-Tr(<(rho)over cap>(H)ln<(rho)over cap>(H)) for the d ensity matrix <(rho)over cap (H)> of a black hole, and S-Rindler(SM) i s the analogous entropy in the Rindler space.