Holonomy groups and spacetimes

TL;DR

This paper investigates the possible holonomy groups of various spacetime models in general relativity, including electromagnetic fields, perfect fluids, scalar fields, Einstein spaces, vacuum, and conformally flat spacetimes, providing new classifications and examples.

Contribution

It introduces new techniques for classifying holonomy groups in diverse spacetime geometries and extends known results to include additional cases like Einstein spaces and specific field configurations.

Findings

Classified holonomy groups for different matter fields in spacetime.

Extended existing results to Einstein spaces and conformally flat spacetimes.

Provided explicit examples illustrating the theoretical classifications.

Abstract

A study is made of the possible holonomy group types of a space-time for which the energy-momentum tensor corresponds to a null or non-null electromagnetic field, a perfect fluid or a massive scalar field. The case of an Einstein space is also included. The techniques developed are also applied to vacuum and conformally flat space-times and contrasted with already known results in these two cases. Examples are given.