Dark Coriolis Fields

TL;DR

This work investigates whether leading-order time-space metric components $g_{ti}$ can produce a Coriolis field within Newton–Cartan gravity that mimics dark matter in disk galaxies. It derives exact dark Coriolis field solutions via a Grad–Shafranov-like decomposition, giving cylindrical and spherical-harmonic forms for the generator $\mathcal{L}_D$ and explicit expressions for the Coriolis field $\boldsymbol{\omega}$, then demonstrates region-specific implementations in the halo, beyond-halo, and bulge to reproduce observed rotation curves. A non-conventional post-Newtonian expansion is developed, linking Newton–Cartan gravity to GR through a dragging velocity $\mathbf{v}_D$ and the relation $\mathbf{g} = -\nabla\Phi + \dot{\mathbf{v}}_D$, $\boldsymbol{\omega} = -\tfrac{1}{2} \nabla\times\mathbf{v}_D$, with leading dynamics $\ddot{\mathbf{x}} = \mathbf{g} + 2\dot{\mathbf{x}}\times\boldsymbol{\omega}$. The results suggest a GR-consistent alternative mechanism for flat galactic rotation curves, while highlighting boundary-condition issues and the need to connect/regenerate the regimes via non-linear corrections and junctions in future work.

Abstract

We argue that the standard post-Newtonian expansion scheme used in General Relativity leaves room for time-space components $g_{ti}$ of the metric to be of the same order of the usual gravitational potential. We explore this possibility and find that such leading order contributions to $g_{ti}$ are related to the Coriolis field of Newton-Cartan gravity. We investigate the possibility that Coriolis fields mimic dark matter effects in disk galaxies. We find solutions from their field equations that sustain the velocity rotation curves in the bulge region and beyond it, notably describing flattish velocity profiles. We dub such solutions Dark Coriolis Fields.