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