## 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.

Original language | English (US) |
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Article number | 104052 |

Journal | Physical Review D |

Volume | 109 |

Issue number | 10 |

DOIs | |

State | Published - May 15 2024 |

## All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics