Towards an interpretation of MOND as a modification of inertia

2015/04/02 by Fathi Namouni, Namouni, Fathi · 1 citation
Physics and Astronomy · #Advanced Differential Geometry Research #Astrophysics of Galaxies (astro-ph.GA) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #astro-ph.GA #gr-qc

paper · pdf · doi:10.48550/arxiv.1504.00475

Revised version, 9 pages, 1 figure. Accepted for publication in Monthly Notices of the Royal Astronomical Society

openalex publication_date 2015/04/02 · arxiv created 2015/06/08 · arxiv updated 2015/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Ma₀log (r/r₀) where a₀ is MOND's acceleration scale and r₀ 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 r₀ 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.

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