Semi-Riemannian structures for symmetric Galilean spacetimes

Abstract

We introduce semi-Riemannian structures well-adapted to certain fields of observers in a Galilean spacetime. The Levi-Civita connection of such a semi-Riemannian metric will allow us to obtain variational characterizations of the Galilean geodesics as well as global results on the topological and differentiable structure of the spacetime. Moreover, these new semi-Riemannian metrics provide a new way to compare the studied Newton–Cartan models with their relativistic counterparts.