{"id":4036,"date":"2026-06-09T18:15:03","date_gmt":"2026-06-10T01:15:03","guid":{"rendered":"https:\/\/coherencegeometry.com\/?p=4036"},"modified":"2026-06-09T19:04:26","modified_gmt":"2026-06-10T02:04:26","slug":"conserved-flux-and-inverse-square-density-profiles-in-galactic-rotation-curves","status":"publish","type":"post","link":"https:\/\/coherencegeometry.com\/index.php\/2026\/06\/09\/conserved-flux-and-inverse-square-density-profiles-in-galactic-rotation-curves\/","title":{"rendered":"Conserved Flux and Inverse-Square Density Profiles in Galactic Rotation Curves"},"content":{"rendered":"\n

Internal ID:<\/strong> CGI-RSR-000029
Author(s):<\/strong> Barry L. Petersen
Document Type:<\/strong> Research Paper
Publication Date:<\/strong> June 2026
Original Creation Date:<\/strong> April 20, 2026
Revised Document Date:<\/strong> June 10, 2026
Status:<\/strong> Public
Domains:<\/strong> Physics
Sub-Domain:<\/strong> Cosmology
Research Topics:<\/strong> Cosmology, Galactic Dynamics, Flux Scaling Model<\/p>\n\n\n\n

Abstract<\/h3>\n\n\n\n


We show that a conserved outward flux in a class of field systems naturally produces an effective mass density scaling as \\(\\rho(r) \\sim r^{-2}\\), leading to flat galactic rotation curves. The result follows directly from Noether energy flux conservation in the exterior region of a localized configuration. Under general conditions, this provides a simple dynamical mechanism for the observed scaling of galactic rotation profiles, without requiring additional particle components or modifications to gravitational dynamics.<\/p>\n\n\n\n

Available Document<\/h3>\n\n\n\n

DOI:<\/strong> 10.5281\/zenodo.20618642<\/code><\/p>\n\n\n\n

Citation:<\/strong>
Petersen, B. L. (2026). Conserved Flux and Inverse-Square Density Profiles in Galactic Rotation Curves. Zenodo. https:\/\/doi.org\/10.5281\/zenodo.20618642<\/a><\/p>\n\n\n\n

Source Code and Supporting Materials<\/h3>\n\n\n\n

N\/A.<\/p>\n\n\n\n

Summary and Notes<\/h3>\n\n\n\n

Core result:<\/em>
The paper establishes the following chain:<\/p>\n\n\n\n

conserved outward flux -> rho(r) ~ r^-2 -> M(r) ~ r -> v(r) approximately constant.<\/p>\n\n\n\n

Under general conditions, inverse-square density profiles and flat galactic rotation curves arise as direct consequences of flux conservation in three-dimensional space.<\/p>\n\n\n\n

Scope:<\/em>
This paper focuses on the dynamical origin of inverse-square density scaling and its connection to galactic rotation curves.<\/p>\n\n\n\n

It does not attempt to provide a complete cosmological model, dark matter theory, structure formation theory, gravitational lensing analysis, or detailed comparison with observational survey data. Its purpose is to isolate and analyze the scaling mechanism itself.<\/p>\n\n\n\n

Relation to subsequent work:<\/em>
This paper forms the first part of a three-paper sequence investigating inverse-square density scaling and its observational consequences.<\/p>\n\n\n\n

Subsequent papers examine gravitational lensing behavior associated with the resulting density profile, and coherence-driven structure formation as a possible source of the conserved exterior flux.<\/p>\n\n\n\n

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

The result is intended to stand independently as a dynamical scaling argument based on conserved outward flux.<\/p>\n\n\n\n

Related Work<\/h3>\n\n\n\n

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

Petersen, B. L. (2026). Constraint-Driven Formation of Coherence Structures and Their Inverse-Square Exterior Flux.<\/em> Zenodo.
https:\/\/doi.org\/10.5281\/zenodo.20618890<\/p>\n\n\n\n","protected":false},"excerpt":{"rendered":"

CGI-RSR-000029 | The paper establishes the following chain: conserved outward flux -> rho(r) ~ r^-2 -> M(r) ~ r -> v(r) approximately constant. Under general conditions, inverse-square density profiles and flat galactic rotation curves arise as direct consequences of flux conservation in
\nthree-dimensional space.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","footnotes":""},"categories":[85,37,31,56],"tags":[],"class_list":["post-4036","post","type-post","status-publish","format-standard","hentry","category-dark-matter","category-cosmology","category-physics","category-research-papers"],"_links":{"self":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/posts\/4036","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/comments?post=4036"}],"version-history":[{"count":3,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/posts\/4036\/revisions"}],"predecessor-version":[{"id":4057,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/posts\/4036\/revisions\/4057"}],"wp:attachment":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/media?parent=4036"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/categories?post=4036"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/tags?post=4036"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}