Journal Article

Quasi-linear formulation of MOND

Mordehai Milgrom

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 403, issue 2, pages 886-895
Published in print April 2010 | ISSN: 0035-8711
Published online March 2010 | e-ISSN: 1365-2966 | DOI:
Quasi-linear formulation of MOND

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A new formulation of modified Newtonian dynamics (MOND) as a modified-potential theory of gravity is propounded. In effect, the theory dictates that the MOND potential φ produced by a mass distribution ρ is a solution of the Poisson equation for the modified source density , where g=ν(|gN|/a0)gN, and gN is the Newtonian acceleration field of ρ. This makes φ simply the scalar potential of the algebraic acceleration field g. The theory thus involves solving only linear-differential equations, with one non-linear, algebraic step. It is derivable from an action, satisfies all the usual conservation laws, and gives the correct centre-of-mass acceleration to composite bodies. The theory is akin in some respects to the non-linear Poisson formulation of Bekenstein and Milgrom, but it is different from it, and is obviously easier to apply. The two theories are shown to emerge as natural modifications of a Palatini-type formulation of Newtonian gravity, and are members in a larger class of bi-potential theories.

Keywords: galaxies: kinematics and dynamics; cosmology: theory; dark matter

Journal Article.  7583 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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