A Unified Perspective on Poincaré and Galilei Relativity: II. General Relativity: A. Kinematics

Journal Article · Tue Aug 05 04:00:00 EDT 2025 · Symmetry

DOI:https://doi.org/10.3390/sym17081245· OSTI ID:2586894

Cardall, Christian Y. ^[1]

---

1. Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Building on the first paper in this series (Paper I), a unified perspective on Poincaré and Galilei physics in a 5-dimensional spacetime setting is further pursued through a consideration of the kinematics of general relativity, with the gravitational dynamics to be addressed separately. The metric of the 5-dimensional affine spacetimes governed by the Bargmann groups considered in Paper I (central extensions of the Poincaré and Galilei groups) is generalized to curved spacetime by extending the usual 1 + 3 (traditionally ‘3 + 1’) formalism of general relativity on 4-dimensional spacetime to a 1 + 3 + 1 formalism, whose spacetime kinematics is shown to be consistent with that of the usual 1 + 3 formalism. Spacetime tensor laws governing the motion of an elementary classical material particle and the dynamics of a simple fluid are presented, along with their 1 + 3 + 1 decompositions; these reference the foliation of spacetime in a manner that partially reverts the Einstein perspective (accelerated fiducial observers, and geodesic material particles and fluid elements) to a Newton-like perspective (geodesic fiducial observers, and accelerated material particles and fluid elements subject to a gravitational force). These spacetime laws of motion for particles and fluids also suggest that a strong-field Galilei general relativity would involve a limit in which not only 𝑐 → ∞ but also 𝐺 → ∞ , such that 𝐺/𝑐² remains constant.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 2586894
• Journal Information: Symmetry, Journal Name: Symmetry Journal Issue: 8 Vol. 17; ISSN 2073-8994
• Publisher: MDPI AG
• Country of Publication: United States
• Language: English

Related Subjects

Bargmann group
Galilei group
Poincaré group
relativity