On the gravitational potential of modified Newtonian dynamics

Abstract

The mathematical structure of the Poisson equation of Modified Newtonian Dynamics (MOND) is studied. The appropriate setting turns out to be an Orlicz-Sobolev space whose Orlicz function is related to Milgrom’s μ-function, where there exists existence and uniqueness of weak solutions. Since these do not have in principle much regularity, a further study is performed where the gravitational field is not too large, where MOND is most relevant. In that case the field turns out to be H¨older continuous. Quasilinear MOND is also analyzed.