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A relativistic description of MOND using the Palatini formalism in an extended metric theory of gravity

  • E. BarrientosEmail author
  • S. Mendoza
Regular Article

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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© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Instituto de AstronomıaUniversidad Nacional Autónoma de MéxicoCiudad de México 04510Mexico

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