A Unified Perspective on Poincaré and Galilei Relativity: II. General Relativity: A. Kinematics
Abstract
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 by 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.
Versions
Related
- A Unified Numerical Study of Axion Stars: From the Nonrelativistic Regime to General Relativity
- From Specific Heat Bounds to Penrose-like Inequalities: A Unified Thermodynamic Perspective
- Fermion−Monopole Scattering: A Unified Perspective
- Entanglement, anti-flatness, and nonlocal nonstabilizerness: a unified perspective from entanglement spectrum
- A Unified Perspective on the Dynamics of Deep Transformers
BibTeX
@misc{cardall2026unified,
title = {{A Unified Perspective on Poincaré and Galilei Relativity: II. General Relativity: A. Kinematics}},
author = {Christian Y. Cardall},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05425},
eprint = {2611.05425},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05425},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Unified Perspective on Poincaré and Galilei Relativity: II. General Relativity: A. Kinematics
AU - Christian Y. Cardall
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.05425
UR - https://arxiv.org/abs/2611.05425
AB - 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 by 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 / c^2 remains constant.
ER -