General Relativistic Rotation Curves in a Post-Newtonian Light

Abstract

The missing of a Keplerian fall-off in the observed galaxy rotation curves represents classical evidence for the existence of dark matter on galactic scales. There has been some recent activity concerning the potential of modelling galactic systems with the help of general relativity. This was motivated by claims that by the use of full general relativity dark matter could be made superfluous. Here we focus on possible axisymmetric and stationary solutions of Einstein's equations with rotating dust. After a short review of the current debate we pursue the idea of approaching such relativistic models in a Newtonian language. We analyse rigidly as well as differentially rotating Newtonian and Post-Newtonian spacetimes and find that it is necessary to incorporate a Post-Newtonian term in order to make physical sense.