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Inverse-Square Density Profiles and Gravitational Lensing from Conserved Flux

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Internal ID: CGI-RSR-000030
Author(s): Barry L. Petersen
Document Type: Research Paper
Publication Date: June 2026
Original Creation Date: April 20, 2026
Revised Document Date: June 10, 2026
Status: Public
Domains: Physics
Sub-Domain: Cosmology
Research Topics: Cosmology, Galactic Dynamics, Flux Scaling Model

Abstract


We examine the gravitational implications of an inverse-square density profile arising from conserved flux in a class of field systems. Starting from \(\rho(r) \sim r^{-2}\), we derive the corresponding gravitational potential and show that it produces lensing signatures consistent with standard halo models. The resulting deflection profile is approximately constant with impact parameter, matching the behavior of isothermal sphere models commonly used in gravitational lensing. This provides a simple dynamical route from flux conservation to observable lensing effects.

Available Document

DOI: 10.5281/zenodo.20618733

Citation:
Petersen, B. L. (2026). Inverse-Square Density Profiles and Gravitational Lensing from Conserved Flux. Zenodo. https://doi.org/10.5281/zenodo.20618733

Source Code and Supporting Materials

N/A

Summary and Notes

Core result:
The paper establishes the following chain:

conserved outward flux -> rho(r) ~ r^-2 -> gravitational potential -> approximately constant lensing deflection.

The resulting lensing behavior is consistent with the leading-order predictions of standard halo models used to interpret gravitational lensing observations.

Scope:
This paper focuses on the lensing consequences of inverse-square density profiles derived from conserved flux.

It does not attempt to provide a complete cosmological model, dark matter theory, structure formation theory, or detailed comparison with observational survey data. Its purpose is to isolate the lensing behavior implied by the scaling mechanism.

Relation to previous work:
This paper builds directly on Conserved Flux and Inverse-Square Density Profiles in Galactic Rotation Curves. That work showed that conserved outward flux naturally produces an effective density profile scaling as rho(r) ~ r^-2 and therefore flat galactic rotation curves.

The present paper examines the corresponding gravitational lensing behavior associated with the same density profile.

Relation to subsequent work:
This paper forms the second part of a three-paper sequence investigating inverse-square density scaling and its observational consequences.

A subsequent paper examines coherence-driven structure formation as a possible source of the conserved exterior flux responsible for the observed scaling behavior.

Relation to Coherence Geometry:
Although motivated in part by broader Coherence Geometry investigations, the derivation presented here is formulated using standard gravitational and field-theoretic concepts and does not require the Coherence Geometry framework for its interpretation.

The result is intended to stand independently as a gravitational lensing analysis of inverse-square density profiles arising from conserved flux.

Related Work

This paper builds directly on:

Petersen, B. L. (2026). Conserved Flux and Inverse-Square Density
Profiles in Galactic Rotation Curves. Zenodo.
https://doi.org/10.5281/zenodo.20618642

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