MOND as the weak field limit of an extended metric theory of gravity with a matter-curvature coupling

Abstract

In this article we construct an extended relativistic f(R) theory of gravity with matter-curvature couplings F(R,L_matt) for which its weak field limit of approximation recovers the simplest version of MOND. We do this by (a) performing an order of magnitude approach and (b) by perturbing the resulting field equations of the theory to the weakest field limit of approximation. We also compute the geodesic equation of the resulting theory and show that it has an extra force, a fact that commonly appears in general matter-curvature couplings. This arxiv version includes a section at the end with an Erratum.

arXiv comment7 pages, accepted for publication in Physical Review D (PRD) Addition of an Erratum at the end of the article has been included

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• Internal kinematics of GAIA DR3 wide binaries: anomalous behaviour in the low acceleration regime
• Challenging a Newtonian prediction through Gaia wide binaries
• Massive white dwarfs in $f(R,L_m)$ gravity
• Stellar structure of quark stars in a modified Starobinsky gravity
• Non-vacuum relativistic extensions of MOND using metric theories of gravity with curvature-matter couplings and their applications to the accelerated expansion of the Universe without dark components
• Dynamics of clusters of galaxies with extended $f(\chi )$ gravity