Non-Metricity Trace Forms and Weak-Field Light Deflection: A Geometric Optical Formulation
Abstract
This paper develops a weak-field, non-metric operational account of gravitational light deflection. In the isotropic formulation of the Schwarzschild weak field, the non-metricity trace 1-forms W and P are computed explicitly and shown to determine the optical response through the exact relation dln n=W−4P, n=g/f. Thus the effective refractive index governing null propagation is not introduced as an external optical analogy, but is tied directly to the trace sector of non-metricity. To connect the trace geometry with matter, an effective scalar calibration potential χ is sourced by an observer-projected macroscopic dilation current, yielding ∇2χ=−κρ in the static weak-field limit. The point-mass calibration fixes Φ=χ/C0≃ 2GM/(rc2), and the resulting optical calculation gives the Eddington deflection angle 4GM/(bc2). The significance of the result is not a modified numerical prediction, but a closed weak-field chain from macroscopic dilation sourcing to non-metricity traces, effective refractive index, and light deflection, without postulating a microscopic deformation law for material rods or clocks.
Related
- Phase-plane formulation of weak gravitational deflection in static spherical spacetimes
- Geometric formulation of state-dependent Langevin dynamics using scalar free energy
- Unsupervised geometric classifier based on optical feature extraction
- Gravitationally-decoupled hairy black holes: probing geometric, optical, and quasinormal mode signatures
- Optical design and characterization of geometric distortion and spatial resolution in lens-enhanced aerial imaging by retro-reflection (LeAIRR)
BibTeX
@misc{ugur2026nonmetricity,
title = {{Non-Metricity Trace Forms and Weak-Field Light Deflection: A Geometric Optical Formulation}},
author = {Sabutay Ugur},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38568},
eprint = {2609.38568},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38568},
}
RIS
TY - UNPB
TI - Non-Metricity Trace Forms and Weak-Field Light Deflection: A Geometric Optical Formulation
AU - Sabutay Ugur
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38568
UR - https://arxiv.org/abs/2609.38568
AB - This paper develops a weak-field, non-metric operational account of gravitational light deflection. In the isotropic formulation of the Schwarzschild weak field, the non-metricity trace 1-forms W and P are computed explicitly and shown to determine the optical response through the exact relation dln n=W−4P, n=g/f. Thus the effective refractive index governing null propagation is not introduced as an external optical analogy, but is tied directly to the trace sector of non-metricity. To connect the trace geometry with matter, an effective scalar calibration potential χ is sourced by an observer-projected macroscopic dilation current, yielding ∇^2χ=−κρ in the static weak-field limit. The point-mass calibration fixes Φ=χ/C_0≃ 2GM/(rc^2), and the resulting optical calculation gives the Eddington deflection angle 4GM/(bc^2). The significance of the result is not a modified numerical prediction, but a closed weak-field chain from macroscopic dilation sourcing to non-metricity traces, effective refractive index, and light deflection, without postulating a microscopic deformation law for material rods or clocks.
ER -