Asymptotic behaviour of curvature and matter in the Penrose limit

TL;DR

This paper investigates the asymptotic behavior of curvature and matter in the Penrose limit, revealing a peeling-off property and analyzing the approach to singularities in cosmological models.

Contribution

It provides a detailed analysis of the asymptotic behavior of Weyl and energy-momentum tensors in the Penrose limit, including examples and implications for cosmological singularities.

Findings

Peeling-off property of tensors in the Penrose limit

Explicit examples with different matter types

Insights into singularity approach in cosmological spacetimes

Abstract

The asymptotic behaviour of the components of the Weyl tensor and of the energy-momentum tensor in the Penrose limit is determined. In both cases a peeling-off property is found. Examples of different types of matter are provided. The expansion and shear of the congruence of null geodesics along which the Penrose limit is taken are determined. Finally, the approach to the singularity in the Penrose limit of cosmological space-times is discussed.