Abstract
The status of the geodesic principle in General Relativity has been a topic of some interest in the recent literature on the foundations of spacetime theories. Part of this discussion has focused on the role that a certain energy condition plays in the proof of a theorem due to Bob Geroch and Pong-Soo Jang [“Motion of a Body in General Relativity.” Journal of Mathematical Physics 16(1) (1975)] that can be taken to make precise the claim that the geodesic principle is a theorem, rather than a postulate, of General Relativity. In this brief note, I show, by explicit counterexample, that not only is a weaker energy condition than the one Geroch and Jang state insufficient to prove the theorem, but in fact a condition still stronger than the one that they assume is necessary.
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I am grateful to David Malament for helpful comments on a previous draft of this paper, including several suggestions both on how to formulate the statements of the propositions in the paper and on how to simplify their proofs. I am also grateful to Bob Geroch and Wayne Myrvold for helpful conversations on topics closely related to this paper.
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Weatherall, J.O. A Brief Remark on Energy Conditions and the Geroch-Jang Theorem. Found Phys 42, 209–214 (2012). https://doi.org/10.1007/s10701-011-9583-y
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DOI: https://doi.org/10.1007/s10701-011-9583-y