Intrinsic, deductive, explicit, and algorithmic characterization of the Szekeres-Szafron solutions

TL;DR

This paper provides an intrinsic, explicit, and algorithmic characterization of the Szekeres-Szafron solutions and their subclasses, including a Rainich-like approach, enhancing understanding of these spacetime metrics.

Contribution

It introduces a new intrinsic and deductive framework for defining and analyzing the Szekeres-Szafron solutions and their subclasses.

Findings

Intrinsic characterization of Szekeres-Szafron solutions

Explicit algorithmic description of subclasses

Rainich-like approach to these metrics

Abstract

We write the known invariant definition of the Szekeres-Szafron family of solutions in an intrinsic, deductive, explicit and algorithmic form. We also intrinsically characterize the two commonly considered subfamilies, and analyze other subclasses, also defined by first-order differential conditions. Furthermore, we present a Rainich-like approach to these metrics.