Generalized Rainich conditions, generalized stress-energy conditions, and the Hawking-Ellis classification

TL;DR

This paper explores the relationships between generalized Rainich conditions, classical energy conditions, and the Hawking-Ellis classification, proposing that Rainich conditions serve as a refinement of existing stress-energy tensor classifications.

Contribution

It clarifies the logical distinctions and interconnections between Rainich conditions, classical energy conditions, and Hawking-Ellis classification, proposing a unified perspective.

Findings

Rainich conditions are algebraic and polynomial in stress-energy tensor.

They are logically distinct from classical energy conditions.

Rainich conditions can be viewed as a refinement of stress-energy classifications.

Abstract

The (generalized) Rainich conditions are algebraic conditions which are polynomial in the (mixed-component) stress-energy tensor. As such they are logically distinct from the usual classical energy conditions (NEC, WEC, SEC, DEC), and logically distinct from the usual Hawking-Ellis (Segr\'e-Pleba\'nski) classification of stress-energy tensors (type I, type II, type III, type IV). There will of course be significant inter-connections between these classification schemes, which we explore in the current article. Overall, we shall argue that it is best to view the (generalized) Rainich conditions as a refinement of the classical energy conditions and the usual Hawking-Ellis classification.