Towards full `Galilei general relativity': Bargmann-Minkowski and Bargmann-Galilei spacetimes

Galilei-Newton spacetime $\mathbb{G}$ with its Galilei group can be understood as a degeneration' as $c \rightarrow \infty$ of Minkowski spacetime $\mathbb{M}$ with its Poincaré group. $\mathbb{G}$ does not have a spacetime metric and its Galilei symmetry transformations do not include energy; but Bargmann-Galilei spacetime $B\mathbb{G}$, a 5-dimensional extension that preserves Galilei physics, remedies these infelicities. Here an analogous Bargmann-Minkowski spacetime $B\mathbb{M}$ is described. While not necessary for Poincaré physics, it may illuminate a path towards a more extensive Galilei general relativity’ than is presently known, which would be a useful – and conceptually and mathematically sound – approximation in astrophysical scenarios such as core-collapse supernovae.