ON THE QUANTIZATION OF CHARGED BLACK-HOLES

The Wheeler-DeWitt equation for the wave function yl of the Schwarzsch ild black hole has been derived by Tomimatsu in the form of a Schrodin ger equation, valid on the apparent horizon, using the two-dimensional Hamiltonian formalism of Hajicek and the radiating Vaidya metric. Her e, the analysis is generalized to the Reissner-Nordstrom black hole. A t constant charge Q, the evaporation rate is calculated from the solut ion for Psi to be (M)over dot = -k(2)r+(-2), where k is a constant and r(+/-) = M +/- root M-2-Q(2) are the radii of the outer event horizon and inner Cauchy horizon. In the extremal limit M --> Q, however, the Hawking temperature T-H = (r(+)- r(-))/4 pi r(+)(2) tends to zero, su ggesting, when the back reaction is taken into account, that the evapo ration cannot occur this way and in agreement with the known dischargi ng process of the hole via the Schwinger electron-positron pair-produc tion mechanism. The more general charged dilaton black holes obtained from the theory L-4 = [R-4-2(del Phi)(2)-e(-2a Phi)F(2)]/16 pi are als o discussed, and it is explained why this quantization procedure canno t be applied when a is non-zero.