DE-BROGLIE-BOHM INTERPRETATION FOR THE WAVE-FUNCTION OF QUANTUM BLACK-HOLES

We study the quantum theory of spherically symmetric black holes. The theory yields the wale function inside the apparent horizon, where the role of time and space coordinates is interchanged. The de Broglie-Bo hm interpretation is applied to the wave function and then the traject ory picture on the minisuperspace is introduced in the quantum as well as the semiclassical region. Around the horizon large quantum fluctua tions on the trajectories of metrics U and V appear in our model, wher e the metrics are functions of the time variable T and are expressed a s ds(2) = -(alpha(2)/U)dT(2) + UdR(2)+ Vd Omega(2). On the trajectorie s, the classical relation U = -V-1/2 + 2Gm holds, and the event horizo n U = 0 corresponds to the classical apparent horizon on V = 2Gm. In o rder to investigate the quantum fluctuation near the horizon, we study a null ray on the dBB trajectory and compare it with the one in the c lassical black hole geometry.