Quantum geometrodynamics for black holes and wormholes

The geometrodynamics of the spherical gravity with a selfgravitating thin dust shell as a source is constructed. The shell Hamiltonian constraint is derived 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, quasicontinuous.Comment: Latex, 32 pages, 5 fig

Dynamics of a thin shell in the Reissner-Nordstrom metric

We describe the dynamics of a thin spherically symmetric gravitating shell in the Reissner-Nordstrom metric of the electrically charged black hole. The energy-momentum tensor of electrically neutral shell is modelled by the perfect fluid with a polytropic equation of state. The motion of a shell is described fully analytically in the particular case of the dust equation of state. We construct the Carter-Penrose diagrams for the global geometry of the eternal black hole, which illustrate all possible types of solutions for moving shell. It is shown that for some specific range of initial parameters there are possible the stable oscillating motion of the shell transferring it consecutively in infinite series of internal universes. We demonstrate also that this oscillating type of motion is possible for an arbitrary polytropic equation of state on the shell.Comment: 17 pages, 7 figure