https://doi.org/10.1140/epjc/s10052-011-1794-z
Regular Article - Theoretical Physics
Recovering MOND from extended metric theories of gravity
1
Instituto de Astronomía, Universidad Nacional Autónoma de México, AP 70-264, Distrito Federal, 04510, Mexico
2
Dipartimento di Scienze Fisiche, Università degli Studi di Napoli “Federico II”, Complesso Universitario di Monte Sant’Angelo, Edificio N, via Cinthia, 80126, Naples, Italy
3
I.N.F.N.—Sezione di Napoli, Complesso Universitario di Monte Sant’Angelo, Edificio G, via Cinthia, 80126, Naples, Italy
4
Departamento de Física, Instituto Nacional de Investigaciones Nucleares, AP 18-1027, Distrito Federal, 11801, Mexico
* e-mail: capozziello@na.infn.it
Received:
16
October
2011
Revised:
25
October
2011
Published online:
9
November
2011
We show that the Modified Newtonian Dynamics (MOND) regime can be fully recovered as the weak-field limit of a particular theory of gravity formulated in the metric approach. This is possible when Milgrom’s acceleration constant is taken as a fundamental quantity which couples to the theory in a very consistent manner. As a consequence, the scale invariance of the gravitational interaction is naturally broken. In this sense, Newtonian gravity is the weak-field limit of general relativity and MOND is the weak-field limit of that particular extended theory of gravity. We also prove that a Noether’s symmetry approach to the problem yields a conserved quantity coherent with this relativistic MONDian extension.
© Springer-Verlag / Società Italiana di Fisica, 2011