Recovering MOND from extended metric theories of gravity

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.

Note:

7 pages, minor corrections to the original version. Accepted for publication in The European Physical Journal C

04.50.Kd
04.25.Nx
95.30.Sf
98.62.Dm
04.20.Fy
98.80.Jk
Alternative theories of gravity
modified Newtonian dynamics
weak-field limit
MOND

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