Quasi-linear formulation of MOND
Abstract
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.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- April 2010
- DOI:
- 10.1111/j.1365-2966.2009.16184.x
- arXiv:
- arXiv:0911.5464
- Bibcode:
- 2010MNRAS.403..886M
- Keywords:
-
- galaxies: kinematics and dynamics;
- cosmology: theory;
- dark matter;
- Astrophysics - Cosmology and Nongalactic Astrophysics;
- General Relativity and Quantum Cosmology
- E-Print:
- 23 pages. Published in MNRAS. Minor changes to match the published version