On the Kuzmin model in fractional Newtonian gravity
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On the Kuzmin model in fractional Newtonian gravity Andrea Giusti1,a
, Roberto Garrappa2,3,b , Geneviève Vachon1,c
1 Physics and Astronomy Department, Bishop’s University, 2600 College Street, Sherbrooke, QC J1M 1Z7,
Canada
2 Department of Mathematics, University of Bari, Via E. Orabona 4, 70126 Bari, Italy 3 The INdAM Research Group GNCS, Istituto Nazionale di Alta Matematica “Francesco Severi”, Piazzale
Aldo Moro 5, 00185 Rome, Italy Received: 18 September 2020 / Accepted: 5 October 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
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.
1 Introduction Galaxy rotation curves and the formation of large-scale structure in the universe are among the most compelling indications that general relativity and the standard model of particle physics cannot account for all natural phenomena. The situation is even more severe than that, indeed it turns out that the theoretical tools which are currently available in physics can only resolve about 5% of the content of the universe. In more detail, in order to explain the current accelerating expansion of the universe it is customary to postulate the existence of an exotic dark energy [1,2] fluid, with positive energy and negative pressure, affecting the universe on its largest scale. Similarly, in order to account for structure formation after the Big Bang, as well as deviations from the expected Newtonian predictions for galaxy rotation curves, it seems to be necessary to include an additional dark component of the universe, featuring no direct coupling with electromagnetic radiation and an (almost) imperceptible pressure, which is dubbed as dark matter [3–5]. In the picture discussed above, dark matter and dark energy are treated as exotic forms of matter evading the Standard Model of particle physics. This exotic matter content finds its way in the so-called standard model of cosmology, also known as the —cold dark matter model or CDM for short, according to which the energy content of the universe splits into a 5% of ordinary (luminous) matter, 25% of dark matter, and about 70% is accounted for by dark energy. It is worth stressing that cold dark matter, namely dark matter moving with non-relativistic velocity, seems to be favored with
a e-mail: [email protected] (corresponding author) b e-mail: [email protected] c e-mail: [email protected]
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Eur. Phys. J. Plus
(2020) 135:79
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