Geometric Asymmetry and Gravitational Fields of Closed Elastic Loops
Abstract
We develop a geometric and variational framework for investigating asymmetric closed elastic loops and their associated gravitational fields. Modeling a loop as a smooth closed curve in Euclidean three-space, we introduce an elastic energy combining line tension and bending rigidity, and consider families of deformations that allow the geometric asymmetry of the loop to be varied. A curvature-weighted effective source, motivated by combining the model's elastic energy density with its axial stress, provides a phenomenological source for a quasi-static Newtonian potential, whose far-field structure can be analyzed through multipole expansions. The asymmetric profiles are treated as instantaneous configurations rather than assumed equilibria. We distinguish this scalar source model from a complete relativistic stress-energy description. We further model branes as embedded manifolds equipped with admissible ambient-diffeomorphism flows. A joint energy functional combining string, brane, and interaction energies defines a variational framework for selecting compatible brane configurations and motivates a coupled gradient-flow model for their dissipative evolution. Finally, we discuss a controlled extension to immersed loops with transverse self-intersections, identifying additional issues involving gravitational self-interaction and topology-changing reconnection. The resulting framework provides a mathematical setting for studying geometric asymmetry, effective gravitational fields, and coupled string-brane deformation, without presupposing a fundamental physical interpretation of the model. Supplementary simulation. A standalone HTML companion lets readers vary the loop parameters, recalculate the elastic energy and curvature-weighted source moments, and compare the direct quasi-static potential with its far-field approximation. The HTML file can be downloaded from the project repository and opened locally: loop-gravity simulation (HTML). Its output illustrates the stated phenomenological model and should not be read as independent validation of its physical assumptions.
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BibTeX
@misc{buchanan2026geometric,
title = {{Geometric Asymmetry and Gravitational Fields of Closed Elastic Loops}},
author = {Ryan J. Buchanan},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.13140/rg.2.2.26448.67847},
url = {https://zenodo.org/records/23580399},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geometric Asymmetry and Gravitational Fields of Closed Elastic Loops
AU - Ryan J. Buchanan
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.13140/rg.2.2.26448.67847
UR - https://zenodo.org/records/23580399
AB - We develop a geometric and variational framework for investigating asymmetric closed elastic loops and their associated gravitational fields. Modeling a loop as a smooth closed curve in Euclidean three-space, we introduce an elastic energy combining line tension and bending rigidity, and consider families of deformations that allow the geometric asymmetry of the loop to be varied. A curvature-weighted effective source, motivated by combining the model's elastic energy density with its axial stress, provides a phenomenological source for a quasi-static Newtonian potential, whose far-field structure can be analyzed through multipole expansions. The asymmetric profiles are treated as instantaneous configurations rather than assumed equilibria. We distinguish this scalar source model from a complete relativistic stress-energy description. We further model branes as embedded manifolds equipped with admissible ambient-diffeomorphism flows. A joint energy functional combining string, brane, and interaction energies defines a variational framework for selecting compatible brane configurations and motivates a coupled gradient-flow model for their dissipative evolution. Finally, we discuss a controlled extension to immersed loops with transverse self-intersections, identifying additional issues involving gravitational self-interaction and topology-changing reconnection. The resulting framework provides a mathematical setting for studying geometric asymmetry, effective gravitational fields, and coupled string-brane deformation, without presupposing a fundamental physical interpretation of the model. Supplementary simulation. A standalone HTML companion lets readers vary the loop parameters, recalculate the elastic energy and curvature-weighted source moments, and compare the direct quasi-static potential with its far-field approximation. The HTML file can be downloaded from the project repository and opened locally: loop-gravity simulation (HTML). Its output illustrates the stated phenomenological model and should not be read as independent validation of its physical assumptions.
ER -