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

Conference · Tue Aug 01 04:00:00 EDT 2023

DOI:https://doi.org/10.1007/978-3-031-38299-4_8· OSTI ID:1999050

Cardall, Christian ^[1]

---

1. ORNL

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.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 1999050
• Country of Publication: United States
• Language: English