Solutions for the modified Newtonian dynamics field equation

Abstract

General properties of the solutions of the modified Newtonian dynamics field equations suggested by Bekenstein and Milgrom (1984) are described along with a numerical scheme for solving this equation for axisymmetric mass configurations, and numerical results are presented. It is demonstrated that the boundary values of interest at infinity determine the solutions of the field equation uniquely, and that for a surface surrounding a finite volume it is the normal component of the 'displacement' vector which has to be given on the surface. The asymptotic dependence on radius of the different angular multipoles of the potential for an arbitrary bound system is deduced. A perturbation formalism is presented which can be used to solve the field equation approximately when the mass distribution involves a small perturbation on a configuration for which the solution is known.