Quantum black holes:unexpected results

Abstract

The quantum black hole model with a self-gravitating spherically symmetric thin dust shell as a source is considered. The shell Hamiltonian constraint is written and the corresponding Schroedinger equation is obtained. This equation appeared to be a finite differences equation. Its solutions are required to be analytic functions on the relevant Riemannian surface. The method of finding discrete spectra is suggested based on the analytic properties of the solutions. The large black hole approximation is considered and the discrete spectra for bound states of quantum black holes and wormholes are found. They depend on two quantum numbers and are, in fact, quasi-continuous. The quantum black hole bound state depends not only on mass but also on an additional quantum number, and black holes with the same mass have different quantum hairs. These hairs exhibit themselves at the Planckian distances near the black hole horizon. For the observer who can not measure the distances smaller than the Planckian length the black hole has the only parameter, its mass. The other, non-measurable, parameter leads to the quantum corrections to the black hole entropy. The quantum states with given mass are the mixed ones. It is shown that there exists the ground quantum black hole state with minimal mass equal approximately the Planckian mass. Its quantum state has zero entropy and it is a pure state. The existence of the quantum hairs may solve (at least partially) the well known information paradox in the black hole physics.