Structure of Malicious Singularities

Details Structure of Malicious Singularities Structure of Malicious Singularities

2002-10-29

arxiv.org/abs/gr-qc/0210100v1

Int.J.Theor.Phys. 42 (2003) 427-441

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, LaTex

Scientific paper

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.

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