Properties of kinematic singularities

TL;DR

This paper investigates kinematic singularities in Bianchi type V cosmological models, showing that certain spacetimes can have bounded curvature tensors and derivatives up to any order at these singularities, challenging traditional notions of singularity behavior.

Contribution

It demonstrates the existence of Bianchi type V spacetimes with kinematic singularities where derivatives of curvature tensors remain bounded to arbitrary order, expanding understanding of singularity properties.

Findings

Existence of spacetimes with bounded curvature derivatives at singularities

Kinematic singularities can be geodesically complete

Boundedness persists for derivatives up to any order

Abstract

The locally rotationally symmetric tilted perfect fluid Bianchi type V cosmological model provides examples of future geodesically complete spacetimes that admit a `kinematic singularity' at which the fluid congruence is inextendible but all frame components of the Weyl and Ricci tensors remain bounded. We show that for any positive integer n there are examples of Bianchi type V spacetimes admitting a kinematic singularity such that the covariant derivatives of the Weyl and Ricci tensors up to the n-th order also stay bounded. We briefly discuss singularities in classical spacetimes.