Reference-renormalized Jacobi primitives for finite-distance massive-particle deflection
Abstract
We develop a reference-renormalized Jacobi-primitive Gauss-Bonnet formalism for finite-distance weak deflection of massive particles in static, spherically symmetric spacetimes. The construction uses the fixed-energy Jacobi metric associated with timelike geodesics and treats the radial curvature primitive as a quantity defined only up to an additive constant. Instead of fixing this constant by requiring the primitive to vanish at a circular timelike orbit, we subtract a reference Jacobi geometry at the same conserved particle energy and impose endpoint normalization on the curvature-density discrepancy. This gives a circular-orbit-free primitive representation of the Gauss-Bonnet curvature contribution while preserving the operational finite-distance definition of the bending angle through local source and receiver directions. We prove that the reference-normalized and circular-orbit-normalized prescriptions agree whenever both are admissible, since their primitives differ only by a constant that cancels from the exact curvature strip integral. The method remains applicable when no admissible circular timelike orbit exists, when the orbit lies outside the Riemannian Jacobi domain, or when the natural no-lens comparison geometry is non-Euclidean. We demonstrate the formalism in three representative settings: Schwarzschild-like bumblebee, Kottler, and Janis-Newman-Winicour (JNW) spacetimes. The formalism therefore identifies circular-orbit anchoring as an auxiliary primitive gauge choice rather than a prerequisite for finite-distance Jacobi Gauss-Bonnet deflection.
Related
- Light deflection in the gravitational field of a solar system body with finite distance of source and observer for sub-micro-arcsecond astrometry
- Reference-covariant optical holonomy in finite-distance black-hole lensing
- Universal Long-distance Tail of Particle-number Density near a Wall in Superfluids
- Analytical framework for computer-generated holography of screen space primitives with point-source integration in the Fourier domain
- Renormalized Polyakov loop in accelerated gluodynamics
BibTeX
@misc{pantig2026referencerenormalized,
title = {{Reference-renormalized Jacobi primitives for finite-distance massive-particle deflection}},
author = {Reggie C. Pantig},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03746},
eprint = {2611.03746},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03746},
}
RIS
TY - UNPB
TI - Reference-renormalized Jacobi primitives for finite-distance massive-particle deflection
AU - Reggie C. Pantig
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03746
UR - https://arxiv.org/abs/2611.03746
AB - We develop a reference-renormalized Jacobi-primitive Gauss-Bonnet formalism for finite-distance weak deflection of massive particles in static, spherically symmetric spacetimes. The construction uses the fixed-energy Jacobi metric associated with timelike geodesics and treats the radial curvature primitive as a quantity defined only up to an additive constant. Instead of fixing this constant by requiring the primitive to vanish at a circular timelike orbit, we subtract a reference Jacobi geometry at the same conserved particle energy and impose endpoint normalization on the curvature-density discrepancy. This gives a circular-orbit-free primitive representation of the Gauss-Bonnet curvature contribution while preserving the operational finite-distance definition of the bending angle through local source and receiver directions. We prove that the reference-normalized and circular-orbit-normalized prescriptions agree whenever both are admissible, since their primitives differ only by a constant that cancels from the exact curvature strip integral. The method remains applicable when no admissible circular timelike orbit exists, when the orbit lies outside the Riemannian Jacobi domain, or when the natural no-lens comparison geometry is non-Euclidean. We demonstrate the formalism in three representative settings: Schwarzschild-like bumblebee, Kottler, and Janis-Newman-Winicour (JNW) spacetimes. The formalism therefore identifies circular-orbit anchoring as an auxiliary primitive gauge choice rather than a prerequisite for finite-distance Jacobi Gauss-Bonnet deflection.
ER -