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

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 (Segré-Plebański) 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.

arXiv commentV1: 20 pages. V2: Matches published version, now 18 pages (new format), minor clarifications added

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• Decomposition of total stress-energy for the generalised Kiselev black hole
• Essential core of the Hawking--Ellis types
• Hawking-Ellis classification of stress-energy: test-fields versus back-reaction
• The type III stress-energy tensor: Ugly Duckling of the Hawking-Ellis classification
• General-relativistic thin-shell Dyson mega-spheres
• Hawking-Ellis type III spacetime geometry
• The spacetime geodesy of perfect fluid spheres
• The eye of the storm: A regular Kerr black hole