General relativity at eleven parameters: gauging the Weyl algebra of a body
Abstract
The companion paper [1] states special relativity for the eleven physically independent quantities of a body, time, position, energy-momentum and spin, and shows that their symmetry is the eleven-generator Weyl algebra P ⊕ M ⊕ D, translations, Lorentz transformations and the dilatation, with the Planck scale entering the relativity principle on the same footing as c. This paper gauges that algebra. The tetrad is the gauge field of P , the spin connection of M , a Weyl vector of D, and a compensator of weight -1 carries the scale; the Weyl algebra is the only eleven-dimensional subalgebra of the conformal algebra that contains the translations, so the gauge group is forced. One experimental fact and one structural one are imposed before the action is written: the gravitational-wave speed bound |c gw /c -1| < 10 -15 and the non-propagation of Einstein-Cartan torsion. The minimal action consistent with both follows a design rule-no kinetic term for anything but the tetrad-which fixes it to 1 2 e [ϕ 2 R(e, ω, b) + αϕ 2 b 2 -λϕ 4 ] + S m , and the constant α drops out of the field equations for spin-1 2 matter. The resulting theory has exactly two propagating degrees of freedom, so c gw = c and γ = β = 1 hold as identities; the compensator is the Stückelberg field of a local symmetry, pure gauge, so there is no fifth force and Newton's constant is its vacuum value, G = c 4 /(8πϕ 2 0 ); in vacuum the theory is Einstein's exactly, so every black-hole exterior is Schwarzschild or Kerr and there are no echoes. All new physics is in matter with spin, where Cartan's algebraic equation produces a contact term -(2πG/c 4 )(s ab s ab -1 2 s 2 ), repulsive for the averaged spin fluid used here. It bounds the density: the modified Friedmann equation H 2 = 8πG 3 ρ(1 -ρ/ρ b ) has the exact dust solution a = (1 + 6πt 2 ) 1/3 , and the bounce, which a non-relativistic estimate places at the Cartan density ρ P (m/M P ) 2 , is in fact Planckian, ρ b ≈ 20ρ P , because the constituents are ultrarelativistic there by (M P /m) 2/3 . A collapsing star has no static core (Buchdahl), bounces inside its horizon in a Planck time, and re-expands into a new region whose Misner-Sharp mass vanished at the turning point: a daughter universe, while the parent keeps a black hole of the original mass; the big bang is the same solution. Mass enters only as the weight-zero number m/M P ; inertial, passive and active mass are one Noether charge, the Eötvös and Nordtvedt parameters vanish identically, and the Eötvös experiment becomes a test of the Weyl invariance of the matter action. The theory is falsified by a gravitational-wave echo, a scalar fifth force, c gw ̸ = c, or a composition-dependent free fall.
Related
- The unified theory at eleven parameters: general relativity and the Standard Model on one algebra
- The eleven parameters of a body: the gauged Weyl algebra, its exact identities and the Palatini form of Higgs inflation
- Special relativity at eleven parameters: the eleven quantities of a body and the Planck constants
- The reverse paradigm: special relativity at eleven parameters with momentum as the base
- Analogue models of gravity at eleven parameters
BibTeX
@misc{reynaud2026general,
title = {{General relativity at eleven parameters: gauging the Weyl algebra of a body}},
author = {Patrick .B Reynaud},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05749758v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - General relativity at eleven parameters: gauging the Weyl algebra of a body
AU - Patrick .B Reynaud
PY - 2026
DA - 2026/09/14
PB - HAL
UR - https://hal.science/hal-05749758v2
AB - The companion paper [1] states special relativity for the eleven physically independent quantities of a body, time, position, energy-momentum and spin, and shows that their symmetry is the eleven-generator Weyl algebra P ⊕ M ⊕ D, translations, Lorentz transformations and the dilatation, with the Planck scale entering the relativity principle on the same footing as c. This paper gauges that algebra. The tetrad is the gauge field of P , the spin connection of M , a Weyl vector of D, and a compensator of weight -1 carries the scale; the Weyl algebra is the only eleven-dimensional subalgebra of the conformal algebra that contains the translations, so the gauge group is forced. One experimental fact and one structural one are imposed before the action is written: the gravitational-wave speed bound |c gw /c -1| < 10 -15 and the non-propagation of Einstein-Cartan torsion. The minimal action consistent with both follows a design rule-no kinetic term for anything but the tetrad-which fixes it to 1 2 e [ϕ 2 R(e, ω, b) + αϕ 2 b 2 -λϕ 4 ] + S m , and the constant α drops out of the field equations for spin-1 2 matter. The resulting theory has exactly two propagating degrees of freedom, so c gw = c and γ = β = 1 hold as identities; the compensator is the Stückelberg field of a local symmetry, pure gauge, so there is no fifth force and Newton's constant is its vacuum value, G = c 4 /(8πϕ 2 0 ); in vacuum the theory is Einstein's exactly, so every black-hole exterior is Schwarzschild or Kerr and there are no echoes. All new physics is in matter with spin, where Cartan's algebraic equation produces a contact term -(2πG/c 4 )(s ab s ab -1 2 s 2 ), repulsive for the averaged spin fluid used here. It bounds the density: the modified Friedmann equation H 2 = 8πG 3 ρ(1 -ρ/ρ b ) has the exact dust solution a = (1 + 6πt 2 ) 1/3 , and the bounce, which a non-relativistic estimate places at the Cartan density ρ P (m/M P ) 2 , is in fact Planckian, ρ b ≈ 20ρ P , because the constituents are ultrarelativistic there by (M P /m) 2/3 . A collapsing star has no static core (Buchdahl), bounces inside its horizon in a Planck time, and re-expands into a new region whose Misner-Sharp mass vanished at the turning point: a daughter universe, while the parent keeps a black hole of the original mass; the big bang is the same solution. Mass enters only as the weight-zero number m/M P ; inertial, passive and active mass are one Noether charge, the Eötvös and Nordtvedt parameters vanish identically, and the Eötvös experiment becomes a test of the Weyl invariance of the matter action. The theory is falsified by a gravitational-wave echo, a scalar fifth force, c gw ̸ = c, or a composition-dependent free fall.
ER -