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On the Kuzmin model in fractional Newtonian gravity

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Abstract

Fractional Newtonian gravity, based on the fractional generalization of Poisson’s equation for Newtonian gravity, is a novel approach to Galactic dynamics aimed at providing an alternative to the dark matter paradigm through a non-local modification of Newton’s theory. We provide an in-depth discussion of the gravitational potential for the Kuzmin disk within this new approach. Specifically, we derive an integral and a series representation for the potential, we verify its asymptotic behavior at large scales, and we provide illuminating plots of the resulting equipotential surfaces.

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Acknowledgements

The work of Roberto Garrappa is supported by a GNCS-INdAM 2020 Project. Andrea Giusti and Geneviève Vachon are supported by the Natural Sciences and Engineering Research Council of Canada (Grant No. 2016-03803 to V. Faraoni) and by Bishop’s University. The work of Andrea Giusti has been carried out in the framework of the activities of the Italian National Group for Mathematical Physics [Gruppo Nazionale per la Fisica Matematica (GNFM) and Istituto Nazionale di Alta Matematica (INdAM)].

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Authors and Affiliations

  1. Physics and Astronomy Department, Bishop’s University, 2600 College Street, Sherbrooke, QC, J1M 1Z7, Canada

    Andrea Giusti & Geneviève Vachon

  2. Department of Mathematics, University of Bari, Via E. Orabona 4, 70126, Bari, Italy

    Roberto Garrappa

  3. The INdAM Research Group GNCS, Istituto Nazionale di Alta Matematica “Francesco Severi”, Piazzale Aldo Moro 5, 00185, Rome, Italy

    Roberto Garrappa

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  1. Andrea Giusti
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Correspondence to Andrea Giusti.

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Giusti, A., Garrappa, R. & Vachon, G. On the Kuzmin model in fractional Newtonian gravity. Eur. Phys. J. Plus 135, 798 (2020). https://doi.org/10.1140/epjp/s13360-020-00831-9

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