Limits of the energy-momentum tensor in general relativity

TL;DR

This paper explores the limits of the energy-momentum tensor in general relativity, extending classification methods and space-time limit concepts to non-vacuum scenarios with a focus on Segre types.

Contribution

It generalizes the coordinate-free approach to include non-vacuum space-times and extends Geroch's work on space-time limits, enhancing tensor classification techniques.

Findings

Developed a limiting diagram for Segre classification

Connected Segre types with Penrose diagrams

Extended Geroch's space-time limit framework

Abstract

A limiting diagram for the Segre classification of the energy-momentum tensor is obtained and discussed in connection with a Penrose specialization diagram for the Segre types. A generalization of the coordinate-free approach to limits of Paiva et al. to include non-vacuum space-times is made. Geroch's work on limits of space-times is also extended. The same argument also justifies part of the procedure for classification of a given spacetime using Cartan scalars.