Segre decomposition of spacetimes

TL;DR

This paper extends a spacetime decomposition method to include Segre types of the Ricci tensor, providing a detailed classification framework based on group actions and tensor properties.

Contribution

It introduces a novel decomposition incorporating Segre types into the existing framework based on Lie-group actions and spacetime properties.

Findings

Decomposition includes Segre types of Ricci tensor.

Applicable to properties depending on continuous endomorphisms.

Enhances classification of spacetimes based on symmetry and tensor types.

Abstract

Following a recent work in which it is shown that a spacetime admitting Lie-group actions may be disjointly decomposed into a a closed subset with no interior plus a dense finite union of open sets in each of which the character and dimension of the group orbits as well as the Petrov type are constant, the aim of this work is to include the Segre types of the Ricci tensor (and hence of the Einstein tensor) into the decomposition. We also show how this type of decomposition can be carried out for any type of property of the spacetime depending on the existence of a continuous endomorphism.