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On the uniqueness of the Newtonian theory as a geometric theory of gravitation

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Abstract

A study is made of geometric theories of gravitation that are consistent with the local validity of Newtonian dynamics. This involves an analysis of the representations of the Galilean group provided by the curvature tensor of a Newtonian spacetime, and by the contravariant mass-momentum tensor. Subject to certain assumptions that are made also in the foundations of general relativity, it is shown that there exists essentially only one such theory that does not place unacceptable restrictions on the mass density of the source. This is the Newtonian theory, generalized by a cosmological term. Any other theory is weaker and is given by a subset of the geometrical equations of the Newtonian theory.

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Authors and Affiliations

  1. Churchill College, University of Cambridge, CB3 ODS, Cambridge, England

    W. G. Dixon

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  1. W. G. Dixon
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Communicated by J. Ehlers

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Dixon, W.G. On the uniqueness of the Newtonian theory as a geometric theory of gravitation. Commun.Math. Phys. 45, 167–182 (1975). https://doi.org/10.1007/BF01629247

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  • DOI: https://doi.org/10.1007/BF01629247

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