Cosserat elasticity as the weak-field limit of Einstein-Cartan relativity
Abstract
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 nonclassical, spin-related fields. It seems that a necessary condition for these results to hold is that one chooses the nonclassical 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.
- Publication:
-
Physical Review D
- Pub Date:
- May 2024
- DOI:
- 10.1103/PhysRevD.109.104052
- arXiv:
- arXiv:2405.12188
- Bibcode:
- 2024PhRvD.109j4052M
- Keywords:
-
- General Relativity and Quantum Cosmology;
- Physics - Geophysics
- E-Print:
- doi:10.1103/PhysRevD.109.104052