On claims that general relativity differs from Newtonian physics for self-gravitating dusts in the low velocity, weak field limit

Abstract

Galaxy rotation curves are generally analyzed theoretically using Newtonian physics; however, two groups of authors have claimed that for self-gravitating dusts, general relativity (GR) makes significantly different predictions to Newtonian physics, even in the weak field, low velocity limit. One group has even gone so far as to claim that nonlinear general relativistic effects can explain flat galactic rotation curves without the need for cold dark matter. These claims seem to contradict the well-known fact that the weak field, low velocity, low pressure correspondence limit of GR is Newtonian gravity, as evidenced by solar system tests. Both groups of authors claim that their conclusions do not contradict this fact, with Cooperstock and Tieu arguing that the reason is that for the solar system, we have test particles orbiting a central gravitating body, whereas for a galaxy, each star is both an orbiting body and a contributor to the net gravitational field, and this supposedly makes a difference due to nonlinear general relativistic effects. Given the significance of these claims for analyses of the flat galactic rotation curve problem, this article compares the predictions of GR and Newtonian gravity for three cases of self-gravitating dusts for which the exact general relativistic solutions are known. These investigations reveal that GR and Newtonian gravity are in excellent agreement in the appropriate limits, thus supporting the conventional use of Newtonian physics to analyze galactic rotation curves. These analyses also reveal some sources of error in the referred to works.