Gomes, Henrique
(2022)
``Is spacetime locally flat?”: a note.
[Preprint]
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 curve we can construct Fermi-coordinates in which Christoffel symbols vanish. They argue, against the orthodoxy, that these senses cannot be given substantive content. I will here, if not entirely disagree, attempt to qualify their verdicts. I also introduce a third sense, based on geodesic deviation: that tidal effects can be ignored, in the sense that deviation becomes linear (i.e. like Minkowski), when geodesics are very close to each other.
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