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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2405.12188 |
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| _version_ | 1866917671131414528 |
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| author | Maitra, Matthew Tromp, Jeroen |
| author_facet | Maitra, Matthew Tromp, Jeroen |
| contents | The weak-field limit of Einstein--Cartan (EC) relativity is studied. The equations of EC theory are rewritten such that they formally resemble those of Einstein General Relativity (EGR); this allows ideas from post-Newtonian theory to be imported without essential change. The equations of motion are then written both at first post-Newtonian (1PN) order and at 1.5PN order. EC theory's 1PN equations of motion are found to be those of a micropolar/Cosserat elastic medium, along with a decoupled evolution equation for non-classical, spin-related fields. It seems that a necessary condition for these results to hold is that one chooses the non-classical fields to scale with the speed of light in a certain empirically reasonable way. Finally, the 1.5PN equations give greater insight into the coupling between energy-momentum and spin within slowly moving, weakly gravitating matter. Specifically, the weakly relativistic modifications to Cosserat theory involve a gravitational torque and an augmentation of the gravitational force due to a `dynamic mass moment density' with an accompanying `dynamic mass moment density flux', and new forms of linear momentum density captured by a `dynamic mass density flux' and a `dynamic momentum density'. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12188 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cosserat elasticity as the weak-field limit of Einstein--Cartan relativity Maitra, Matthew Tromp, Jeroen General Relativity and Quantum Cosmology Geophysics The weak-field limit of Einstein--Cartan (EC) relativity is studied. The equations of EC theory are rewritten such that they formally resemble those of Einstein General Relativity (EGR); this allows ideas from post-Newtonian theory to be imported without essential change. The equations of motion are then written both at first post-Newtonian (1PN) order and at 1.5PN order. EC theory's 1PN equations of motion are found to be those of a micropolar/Cosserat elastic medium, along with a decoupled evolution equation for non-classical, spin-related fields. It seems that a necessary condition for these results to hold is that one chooses the non-classical fields to scale with the speed of light in a certain empirically reasonable way. Finally, the 1.5PN equations give greater insight into the coupling between energy-momentum and spin within slowly moving, weakly gravitating matter. Specifically, the weakly relativistic modifications to Cosserat theory involve a gravitational torque and an augmentation of the gravitational force due to a `dynamic mass moment density' with an accompanying `dynamic mass moment density flux', and new forms of linear momentum density captured by a `dynamic mass density flux' and a `dynamic momentum density'. |
| title | Cosserat elasticity as the weak-field limit of Einstein--Cartan relativity |
| topic | General Relativity and Quantum Cosmology Geophysics |
| url | https://arxiv.org/abs/2405.12188 |