ON A QUANTUM-MECHANICAL MODEL OF A BLACK-HOLE

A quantum mechanical model of a Schwarzschild black hole is constructed. This model is based on the simplest classical model, namely, a spherical thin dust shell as a source for a black hole mass. Such a mechanical system has only one degree of freedom which is quantized. The Klein-Gordon-type equation obtained exhibits some interesting features. This equation is an equation in finite differences and not a differential equation. There are nonlocalities near the singularities (r = 0) and at the horizon. For the large black holes this equation can be approximated by an ordinary differential equation, which has one solution in the interior regions of a black hole. This is an ingoing wave in the collapse region and an outgoing wave in the anticollapse regions. An approximate expression for the bound states is obtained. © 1990.