{
  "id": "1504.00475",
  "version": "v1",
  "published": "2015-04-02T08:46:26.000Z",
  "updated": "2015-04-02T08:46:26.000Z",
  "title": "Towards an interpretation of MOND as a modification of inertia",
  "authors": [
    "Fathi Namouni"
  ],
  "categories": [
    "astro-ph.GA",
    "gr-qc"
  ],
  "abstract": "We explore the possibility that Milgrom's Modified Newtonian Dynamics (MOND) is a manifestation of the modification of inertia at small accelerations. Consistent with the Tully-Fisher relation, dynamics in the small acceleration domain may originate from a quartic (cubic) velocity-dependence of energy (momentum) whereas gravitational potentials remain linear with respect to mass. The natural framework for this interpretation is Finsler geometry. The simplest static isotropic Finsler metric of a gravitating mass that incorporates the Tully-Fisher relation at small acceleration is associated with a spacetime interval that is either a homogeneous quartic root of polynomials of local displacements or a simple root of a rational fraction thereof. We determine the low energy gravitational equation and find that Finsler spacetimes that produce a Tully-Fisher relation require that the gravitational potential be modified. For an isolated mass, Newton's potential $Mr^{-1}$ is replaced by $Ma_0\\log (r/r_0)$ where $a_0$ is MOND's acceleration scale and $r_0$ is a yet undetermined distance scale. Orbital energy is linear with respect to mass but angular momentum is proportional to $ M^{3/4}$. Asymptotic light deflection resulting from time curvature is similar to that of a singular isothermal sphere implying that space curvature must be the main source of deflection in static Finsler spacetimes possibly through the presence of the distance scale $r_0$ that appears in the asymptotic form of the gravitational potential. The quartic nature of the Finsler metric hints at the existence of an underlying area-metric that describes the effective structure of spacetime.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-02T08:46:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tully-fisher relation",
      "small acceleration",
      "interpretation",
      "simplest static isotropic finsler metric",
      "modification"
    ],
    "publication": {
      "doi": "10.1093/mnras/stv1292"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1357579
    }
  }
}