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 $\Gamma =E\times G$, 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 $\Gamma$ 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.

18 pages, LaTex

References in corpus (2)

• Origin of Classical Singularities
• Generalized Strong Curvature Singularities and Cosmic Censorship

Cited by in corpus (2)

• Conceptual Unification of Gravity and Quanta
• Anatomy of Malicious Singularities