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Towards Full ‘Galilei General Relativity’: Bargmann-Minkowski and Bargmann-Galilei Spacetimes...

by Christian Y Cardall
Publication Type
Conference Paper
Book Title
Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science
Publication Date
Page Numbers
69 to 78
Publisher Location
Cham, Switzerland
Conference Name
GSI'23, 6th International Conference on Geometric Science of Information, Saint-Malo, Palais du Grand Large, France, 30 Aug - 1 Sep 2023
Conference Location
Saint-Malo, France
Conference Sponsor
SEE: Société de l’électricité, de l’électronique et des technologies de l’information et de la communication
Conference Date

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.