Abstract.
We construct a relativistic metric description of MOND using the Palatini formalism following the \(f(\chi) = \chi^{b}\) description of T. Bernal et al. (Eur. Phys. J. C 71, 1794 (2011)). We show that in order to recover the non-relativistic MOND regime where, for circular orbits the Tully-Fisher law replaces Kepler’s third law, the value of the parameter \( b = 3/2\), which is coincident with the value found using the pure metric formalism of T. Bernal et al. Unlike this pure metric formalism, which yields fourth-order field equations, the Palatini approach yields second-order field equations, which is a desirable requirement from a theoretical perspective. Thus, the phenomenology associated to astrophysical phenomena with Tully-Fisher scalings can be accounted for using this proposal, without the need to introduce any non-baryonic dark matter particles.
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Barrientos, E., Mendoza, S. A relativistic description of MOND using the Palatini formalism in an extended metric theory of gravity. Eur. Phys. J. Plus 131, 367 (2016). https://doi.org/10.1140/epjp/i2016-16367-0
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DOI: https://doi.org/10.1140/epjp/i2016-16367-0