  Recently it was proposed to explain the dynamical origin of the entropy of a
black hole by identifying its dynamical degrees of freedom with states of
quantum fields propagating in the black-hole's interior. The present paper
contains the further development of this approach. The no-boundary proposal
(analogous to the Hartle-Hawking no-boundary proposal in quantum cosmology) is
put forward for defining the wave function of a black hole. This wave function
is a functional on the configuration space of physical fields (including the
gravitational one) on the three-dimensional space with the Einstein-Rosen
bridge topology.It is shown that in the limit of small perturbations on the
Kruskal background geometry the no-boundary wave function coincides with the
Hartle-Hawking vacuum state. The invariant definition of inside and outside
modes is proposed. The density matrix describing the internal state of a black
hole is obtained by averaging over the outside modes. This density matrix is
used to define the entropy of a black hole, which is to be divergent. It is
argued that the quantum fluctuations of the horizon which are internally
present in the proposed formalism may give the necessary cut-off and provide a
black hole with the finite entropy.
