Wolf, William J. and Read, James and Vigneron, Quentin (2023) The Non-Relativistic Geometric Trinity of Gravity. [Preprint]

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Abstract

The geometric trinity of gravity comprises three distinct formulations of general relativity: (i) the standard formulation which interprets gravity in terms of spacetime curvature, (ii) the teleparallel equivalent of general relativity which interprets gravity in terms of spacetime torsion, and (iii) the symmetric teleparallel equivalent of general relativity (STEGR) which interprets gravity in terms of spacetime non-metricity. In this article, we complete a non-relativistic geometric trinity of gravity, by (a) taking the non-relativistic limit of STEGR to determine its non-relativistic analogue, and (b) demonstrating that this non-metric theory is equivalent to Newton--Cartan theory and its teleparallel equivalent, i.e., the standard curvature and torsion based theories in the non-relativistic regime that are both geometrised versions of classical Newtonian gravity.

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Item Type:	Preprint
Creators:	Creators Email ORCID Wolf, William J. williamjwolf2@gmail.com Read, James james.read@philosophy.ox.ac.uk Vigneron, Quentin quentin.vigneron@umk.pl
Additional Information:	Comments welcome! 26 pages. This is a substantially revised and expanded version of the previous draft. In previous versions, we took the non-relativistic limit of STEGR assuming that non-metricity took a Weylian form. We have included this result here as a special case, but significantly expanded the article to include the non-relativistic limit of STEGR in full generality as well as further discussions.
Keywords:	Geometric Trinity, Non-metricity, Non-relativistic limits, Curvature, Torsion, Non-relavistic gravity, Newton-Cartan Theory, Teleparallel Gravity
Subjects:	Specific Sciences > Physics Specific Sciences > Physics > Relativity Theory
Depositing User:	Mr. William Wolf
Date Deposited:	28 Dec 2023 17:44
Last Modified:	28 Dec 2023 17:44
Item ID:	22894
Subjects:	Specific Sciences > Physics Specific Sciences > Physics > Relativity Theory
Date:	26 December 2023
URI:	https://philsci-archive.pitt.edu/id/eprint/22894

Available Versions of this Item

• The Non-Relativistic Geometric Trinity of Gravity. (deposited 15 Aug 2023 14:01)
  • The Non-Relativistic Geometric Trinity of Gravity. (deposited 28 Dec 2023 17:44) [Currently Displayed]

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