Deformation-Field Gravity from a $GL(4,\mathbb R)$ Gravitational Potential Tensor
Year: 2026
Type: preprint
Abstract: A classical deformation-field formulation of gravity is developed from one invertible potential tensor $A$ on a physical Minkowski reference. On a Lorentz-polar admissible domain, $A=OP$ induces $g=P^T\eta P$ and transports the reference connection by $\nabla^A_XY=A^{-1}\bar\nabla_X(AY)$. The orthogonal factor $O$ is distinguished from the frame reorientation already produced by anisotropic dilation and shear in $P$. The relative distortion splits as $D_A=D_P+D_O$: $D_P$ compares deformation transport with the Levi-Civita transport of the induced metric, whereas $D_O$ is the additional connection change at fixed metric. For a Levi-Civita reference, $D_P$ is the contortion expression of the Codazzi compatibility defect. With fixed curvature, matter, and boundary conventions, the distortion action is Einstein--Hilbert equivalent. Its metric-coupled branch has two tensor helicities and contains the exterior Fock solution in the harmonic reference representation. The general $O$ sector is retained as orientation structure whose dynamical status is determined by the chosen complete action; the minimal metric-coupled action supplies no independent $O$ kinetic mode. A wave-like condition selecting an orientation representative is therefore distinguished from an Euler equation. Connection-sensitive matter or additional modes require a specified dynamical completion. Curved references and successive or parameter-dependent deformations are admitted geometrically without replacing the physical Minkowski background of this model.
Author: Liu, Gordon (刘清涛)
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165159985
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