Quasi-linear formulation of MOND

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 phi produced by a mass distribution. is a solution of the Poisson equation for the modified source density (rho) over cap = -(4 pi G)(-1) del.g, where g = nu(vertical bar g(N)vertical bar/a(0))g(N), and g(N) is the Newtonian acceleration field of rho. This makes phi 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.