Unfolding the singularities in superspace
The superspace of a three dimensional compact connected Riemannian manifold M is the space of all Riemannian geometries of M modulo the group of diffeomorphisms of M. The superspace is the configuration space for the dynamical formulation of classical general relativity and the domain space for the quantum mechanical state functional in quantum gravity. The superspace is not a manifold, having singularities arising from the varying dimensions of the isometry groups of the different metrics. Here a construction is described for unfolding the singularities of superspace. The resulting (unfolded) space is a singularity free infinite dimensional manifold and the construction is natural, covariant with respect to all coordinate transformations, and it does not exclude any particular highly symmetrical solution from superspace. The relationship between the proposed unfolding construction and a previous one based on the choice of a particular point is also discussed.
scientific article; zbMATH DE number 3860022