We show that modified Newtonian dynamics (MOND) predicts distinct galactic acceleration curve geometries - in the space of total observed centripetal accelerations, gtot, versus the inferred Newtonian acceleration from baryonic matter, gN, which we refer to as g2 space - and corresponding rotation speed curves. MOND modified gravity predicts cored geometries for isolated galaxies, while MOND modified inertia yields neutral geometries (i.e. neither cuspy nor cored), based on a cusp-core classification of galaxy rotation curve geometry in g2 space, rather than on inferred dark matter (DM) density profiles. The classification can be applied both to DM and modified gravity models as well as data and implies a 'cusp-core' challenge for MOND from observations (e.g., of cuspy galaxies), which is different from the so-called cusp-core problem of DM. We illustrate this challenge with a number of cuspy and cored galaxies from the SPARC rotation curve database that deviate significantly from the MOND modified gravity and MOND modified inertia predictions.
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Acknowledgements. We thank J. Read, W.-C. Huang and J. Smirnov for discussions and comments on the draft. The authors acknowledge partial funding from The Council For Independent Research, grant number DFF 6108-00623. The CP3-Origins center is partially funded by the Danish National Research Foundation, grant number DNRF90.
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