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.
 Publication:

The Astrophysical Journal
 Pub Date:
 March 1986
 DOI:
 10.1086/164021
 Bibcode:
 1986ApJ...302..617M
 Keywords:

 Computational Astrophysics;
 Cosmology;
 Field Theory (Physics);
 Galactic Rotation;
 Newton Theory;
 Acceleration (Physics);
 Boundary Value Problems;
 Difference Equations;
 Disk Galaxies;
 Mass Distribution;
 Perturbation Theory;
 Stellar Motions;
 Astrophysics;
 COSMOLOGY;
 STARS: STELLAR DYNAMICS