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

The "ugly duckling"of the Segré-Plebański-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 realizations 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.