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``Is spacetime locally flat?”: a note

Gomes, Henrique (2025) ``Is spacetime locally flat?”: a note. Philosophy of Physics. ISSN 2753-5908

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Abstract

I review three senses in which the slogans, `spacetime is locally flat’, and-or ‘spacetime is locally approximately flat’ can be justified. The background is a recent paper of Fletcher and Weatherall, that focuses on two of these senses: (i) that each tangent space is `like Minkowski', and (ii) that around any geodesic we can construct Riemann-normal-coordinates in which Christoffel symbols vanish. They argue, against the orthodoxy, that these senses cannot be given a substantive content. I will here, if not entirely disagree, attempt to qualify their verdicts about (i) and (ii). I will also introduce a third sense, which I take to be the most cogent defense of the special role played by Minkowski spacetime in general relativity. This sense of local flatness concerns the extent to which tidal effects can be ignored, i.e. the extent to which deviation becomes linear (i.e. like Minkowski), when geodesics are very close to each other.

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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Gomes, Henriquegomes.ha@gmail.com0000-0002-9285-0090
Keywords: Relativity
Subjects: Specific Sciences > Physics > Relativity Theory
Depositing User: Dr Henrique Gomes
Date Deposited: 24 Sep 2025 11:13
Last Modified: 24 Sep 2025 11:13
Item ID: 26730
Journal or Publication Title: Philosophy of Physics
Publisher: LSE Press
Subjects: Specific Sciences > Physics > Relativity Theory
Date: 2025
ISSN: 2753-5908
URI: https://philsci-archive.pitt.edu/id/eprint/26730

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