Realisations of type III stress-energy tensors of the Hawking-Ellis classification in scalar-tensor gravity

TL;DR

This paper demonstrates the physical realization of type III stress-energy tensors within scalar-tensor and Horndeski gravity theories, challenging previous beliefs about their impossibility in Einstein gravity.

Contribution

It introduces a class of type III stress-energy tensor solutions in scalar-tensor and Horndeski gravity, expanding the understanding of possible stress-energy configurations.

Findings

Type III tensors realized in scalar-tensor gravity

Physical interpretation of these tensors provided

Challenges the notion of impossibility in Einstein gravity

Abstract

The ``ugly duckling'' of the Segr\'e-Pleba\'nski-Hawking-Ellis classification of stress-energy tensors is believed to be either impossible or extremely difficult to realise in Einstein gravity. Effective stress-energy tensors in alternative gravity offer a wider range of possibilities. We report a class of type III realisations in ``first-generation'' scalar-tensor and in Horndeski gravity, and their physical interpretation. The ugly duckling may be a freak of nature of limited importance but it is not physically impossible.