The hole argument meets Noether's theorem

Henrique Gomes

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arXiv · 2403.10970

The hole argument meets Noether's theorem

Henrique Gomes

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Abstract

The hole argument of general relativity threatens a radical and pernicious form of indeterminism. One natural response to the argument is that points belonging to different but isometric models should always be identified, or 'dragged-along', by the diffeomorphism that relates them. In this paper, I first criticise this response and its construal of isometry: it stumbles on certain cases, like Noether's second theorem. Then I go on to describe how the essential features of Einstein\rq{}s `point-coincidence' response to the hole argument avoid the criticisms of the `drag-along response' and are compatible with Noether's second theorem.

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Henrique Gomes. 2024-03-16. The hole argument meets Noether's theorem. https://arxiv.org/abs/2403.10970

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