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arXiv · 2305.18428

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

Christian Y. Cardall
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Abstract

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 Poincar\'e 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 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 astrophysical scenarios such as core-collapse supernovae.

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Christian Y. Cardall. 2023-05-28. Towards full `Galilei general relativity': Bargmann-Minkowski and Bargmann-Galilei spacetimes. https://arxiv.org/abs/2305.18428

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