Origin of Classical Singularities

Abstract

We briefly review some results concerning the problem of classical singularities in general relativity, obtained with the help of the theory of differential spaces. In this theory one studies a given space in terms of functional algebras defined on it. Then we present a generalization of this method consisting in changing from functional (commutative) algebras to noncommutative algebras. By representing such an algebra as a space of operators on a Hilbert space we study the existence and properties of various kinds of singular space-times. The obtained results suggest that in the noncommutative regime, supposedly reigning in the pre-Planck era, there is no distinction between singular and non-singular states of the universe, and that classical singularities are produced in the transition process from noncommutative geometry to the standard space-time physics.

19 pages, latex, no figures

References in corpus (3)

• An Introduction to Noncommutative Spaces and their Geometry
• Towards Noncommutative Quantization of Gravity
• Emergence of Time

Cited by in corpus (7)

• Conceptual Unification of Gravity and Quanta
• Quantization and spacetime topology
• State Vector Reduction as a Shadow of a Noncommutative Dynamics
• Anatomy of Malicious Singularities
• Structure of Malicious Singularities
• Nonlocal Phenomena from Noncommutative Pre-Planckian Regime
• Smooth Beginning of the Universe