Towards an interpretation of MOND as a modification of inertia
  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.
