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Galilei-Newton spacetime $\mathbb{G}$ with its Galilei group can beunderstood as a `degeneration' as $c \rightarrow \infty$ of Minkowski spacetime$\mathbb{M}$ with its Poincar\'e group. $\mathbb{G}$ does not have a spacetimemetric and its Galilei symmetry transformations do not include energy; butBargmann-Galilei spacetime $B\mathbb{G}$, a 5-dimensional extension thatpreserves Galilei physics, remedies these infelicities. Here an analogousBargmann-Minkowski spacetime $B\mathbb{M}$ is described. While not necessaryfor Poincar\'e 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 astrophysicalscenarios such as core-collapse supernovae.

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