Quasi-linear formulation of MOND
  A new formulation of 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 rho is a solution of the Poisson equation for the
modified source density rho*=-(1/4 pi G)divergence(g), where g=nu(|gN|/a0)gN,
and gN 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 nonlinear,
algebraic step. It is derivable from an action, satisfies all the usual
conservation laws, and gives the correct center-of-mass acceleration to
composite bodies. The theory is akin in some respects to the nonlinear 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.
