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We investigate a quantum cosmological model consisting of inhomogeneous massless minimally coupled scalar field perturbations on a closed Friedmann-Robertson-Walker minisuperspace model with a spatially homogeneous massless minimally coupled scalar field. We discuss how to define a reduced density matrix by summing over the perturbations in the full density matrix, using the approximate Hilbert-space structure that exists for the perturbation wave function when the minisuperspace part of the wave function is of the WKB form. We then concentrate on two particular candidates for a reduced density matrix and discuss their relation to particle creation effects in quantum field theory on curved spacetime. Our results do not suggest that decoherence in the reduced density matrices could be directly identified as a lack of interference between the classical trajectories that correspond to a WKB minisuperspace part of the total wave function.

We investigate the retrieval of classical behavior from the wave function of the Universe. It has been previously argued that to do this two conditions are necessary: decoherence (or lack of quantum interference) and the existence of classical correlations. Using the Wigner function we study the mutual compatibility of these requirements. Assuming the correlation interpretation of Geroch and Hartle, we show that some form of coarse graining is essential for the theory to predict classical behavior from WKB wave functions. We also show that there must be a compromise between the degree of decoherence and the sharpness of classical correlations. A minisuperspace model is used as an example to illustrate these points.

The wave function of the Universe defined by the Hartle-Hawking proposal is studied for two minisuperspace models, the Friedmann-Robertson-Walker universe with a massive scalar field and the anisotropic Kantowski-Sachs cosmology. Solutions of the Wheeler-DeWitt equation are evaluated numerically. We also examine the trajectories to which these correspond in the classical limit. Attention is focused on the fact that most classical trajectories recollapse to a singularity. They will add an oscillatory component to the wave function in the region of small three-volume where it is predominantly exponential. They will thus modify the original boundary conditions. The Kantowski-Sachs universes generically evolve from isotropy during expansion to increasing anisotropy during recollapse, ending as a black-hole interior. We comment, therefore, on the arrow of time naturally induced by the Hartle-Hawking proposal.

We show that the Schwarzschild black hole extended to five dimensions by the addition of an extra dimension is stable against linearized perturbations of the metric; thus the topology of the horizon can be thought of as an extra black-hole hair.

We solve the Euclidean Einstein equations with three-index antisymmetric and two-index antisymmetric (electromagnetic) tensors for monopole configurations on a space with three-surfaces of topology {ital S}{sup 1}{times}{ital S}{sup 2} and describe wormhole solutions. We show that these wormholes and the one of Giddings and Strominger, Hawking, Halliwell and Laflamme, and Myers can be obtained by slicing five-dimensional spaces with horizons.