Quasilocal Newtonian limit of general relativity and galactic dynamics

Abstract

We present a new self-consistent perturbative expansion for realistic isolated differentially rotating systems—disc galaxies. At leading order it is formally equivalent to Ehlers’ Newton–Cartan limit, which we reinterpret in terms of quasilocal energy and angular momentum. The self-consistent coupling of these quasilocal terms leads to first-order differences from the conventional Newtonian limit. A modified Poisson equation is obtained, along with modifications to the equations of motion for the effective fluid elements. By fitting to astrophysical data, we show that the phenomenology of collisionless dark matter for disc galaxies can be reproduced. Potential important consequences for gravitational physics on galactic and cosmological scales are briefly discussed.