Stated loosely, the geodesic hypothesis says that test particles follow geodesics, where "test particle" means it has to be small in some sense (size, mass, ...), and there is an ambiguity in the word "geodesics" because we want to talk about geodesics of the spacetime that would have existed without the test particle. If we don't make any assumption about the matter field that the test particle is built out of, then there are counterexamples to the geodesic hypothesis.(adsbygoogle = window.adsbygoogle || []).push({});

The best references I know of for the current state of the art on this hypothesis are:

Yang, http://arxiv.org/abs/1209.3985

Ehlers and Geroch, http://arxiv.org/abs/gr-qc/0309074v1

Ehlers assumes an energy condition. Yang assumes that the matter field works according to the Klein-Gordon equation. I wrote up a presentation of the Ehlers-Geroch ideas, using crayons, here: http://www.lightandmatter.com/html_books/genrel/ch08/ch08.html#Section8.1 [Broken] (subsection 8.1.3).

Is one of these results weaker or stronger than the other? Naively, I would imagine that if something is a solution of the Klein-Gordon equation with mass m, then ... well, m is positive, so it satisfies energy conditions, doesn't it? Which energy conditions,...er, I don't know.

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# State of the art re the geodesic hypothesis

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