Limits of space-times in five dimensions and their relation to the Segre Types

TL;DR

This paper extends the Segre classification limits to five-dimensional space-times, connecting them with energy-momentum tensor limits and generalizing Geroch's results to Kaluza-Klein models.

Contribution

It introduces a limiting diagram for Segre types in 5D space-times and generalizes existing 4D results to higher-dimensional Kaluza-Klein frameworks.

Findings

Established a limiting diagram for 5D Segre classification.

Extended Geroch's limits to five-dimensional Kaluza-Klein space-times.

Connected Segre classification limits with energy-momentum tensor limits.

Abstract

A limiting diagram for the Segre classification in 5-dimensional space-times is obtained, extending a recent work on limits of the energy-momentum tensor in general relativity. Some of Geroch's results on limits of space-times in general relativity are also extended to the context of five-dimensional Kaluza-Klein space-times.