Dark Coriolis fields

In the framework of Newton-Cartan gravity, we investigate whether configurations of the Coriolis Field exist that can mimic dark matter effects in disk galaxies. We find solutions to the field equations and the equations of motion that yield a velocity profile qualitatively compatible with the observed rotational velocity curves. We dub such solutions for the Coriolis Fields Dark Coriolis Fields. In the second part of the paper, we interpret our results within a non-conventional post-Newtonian approach, noting that in the standard post-Newtonian expansion procedure used in General Relativity, there is room for the time-space components of the metric gti\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{ti}$$\end{document} to be of the same order as the usual gravitational potential gtt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{tt}$$\end{document}. When this possibility is taken into account, it turns out that such leading order contributions to gti\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{ti}$$\end{document} are precisely the vector potential of the Coriolis field.