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 describing gravity in terms of spacetime curvature, (ii) the teleparallel equivalent of general relativity describing gravity in terms of spacetime torsion, and (iii) the symmetric teleparallel equivalent of general relativity (STEGR) describing gravity in terms of spacetime non-metricity. In this article, we complete a geometric trinity of non-relativistic 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 the Newton--Cartan theory and its teleparallel equivalent, i.e., the curvature and the torsion based non-relativistic theories 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:	Accepted version to appear in General Relativity and Gravitation
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:	26 Sep 2024 12:49
Last Modified:	26 Sep 2024 12:49
Item ID:	23954
Subjects:	Specific Sciences > Physics Specific Sciences > Physics > Relativity Theory
Date:	26 December 2023
URI:	https://philsci-archive.pitt.edu/id/eprint/23954

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)
    • The Non-Relativistic Geometric Trinity of Gravity. (deposited 26 Sep 2024 12:49) [Currently Displayed]

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