Eur. Phys. J. Plus (2016) 131: 367
https://doi.org/10.1140/epjp/i2016-16367-0

Regular Article

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

Instituto de Astronomıa, Universidad Nacional Autónoma de México, AP 70-264, Ciudad de México 04510, Mexico

^* e-mail: ebarrientos@astro.unam.mx

Received: 27 June 2016
Accepted: 23 September 2016
Published online: 19 October 2016

Abstract

We construct a relativistic metric description of MOND using the Palatini formalism following the 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 , 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.