The non-relativistic geometric trinity of gravity
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 symmet...
| Main Authors: | , , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
Springer
2024
|
| _version_ | 1817931045075419136 |
|---|---|
| author | Wolf, WJ Read, J Vigneron, Q |
| author_facet | Wolf, WJ Read, J Vigneron, Q |
| author_sort | Wolf, WJ |
| collection | OXFORD |
| description | 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 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. |
| first_indexed | 2024-12-09T03:15:46Z |
| format | Journal article |
| id | oxford-uuid:141300a0-2dc6-4640-90ec-1a43c0961d16 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:15:46Z |
| publishDate | 2024 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:141300a0-2dc6-4640-90ec-1a43c0961d162024-10-19T20:09:18ZThe non-relativistic geometric trinity of gravityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:141300a0-2dc6-4640-90ec-1a43c0961d16EnglishJisc Publications RouterSpringer2024Wolf, WJRead, JVigneron, QThe 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 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. |
| spellingShingle | Wolf, WJ Read, J Vigneron, Q The non-relativistic geometric trinity of gravity |
| title | The non-relativistic geometric trinity of gravity |
| title_full | The non-relativistic geometric trinity of gravity |
| title_fullStr | The non-relativistic geometric trinity of gravity |
| title_full_unstemmed | The non-relativistic geometric trinity of gravity |
| title_short | The non-relativistic geometric trinity of gravity |
| title_sort | non relativistic geometric trinity of gravity |
| work_keys_str_mv | AT wolfwj thenonrelativisticgeometrictrinityofgravity AT readj thenonrelativisticgeometrictrinityofgravity AT vigneronq thenonrelativisticgeometrictrinityofgravity AT wolfwj nonrelativisticgeometrictrinityofgravity AT readj nonrelativisticgeometrictrinityofgravity AT vigneronq nonrelativisticgeometrictrinityofgravity |