Structure of Malicious Singularities

Abstract

We investigate spacetimes with their singular boundaries as noncommutative spaces. Such a space is defined by a noncommutative algebra on a transformation groupoid $Γ= E \times G$, where $E$ is the total space of the frame bundle over spacetime with its singular boundary, and $G$ its structural group. There is a bijective correspondence between unitary representations of the groupoid $Γ$ and the systems of imprimitivity of the group $G$. This allows us to apply the Mackey theorem, and deduce from it some information concerning singular fibres of the groupoid. A subgroup $K$ of $G$, from which -- according to the Mackey theorem -- the representation is induced to the whole of $G$, can be regarded as measuring the "richness" of the singularity structure.