{"id":3389,"date":"2026-05-18T01:10:03","date_gmt":"2026-05-18T08:10:03","guid":{"rendered":"https:\/\/coherencegeometry.com\/?p=3389"},"modified":"2026-05-18T07:22:15","modified_gmt":"2026-05-18T14:22:15","slug":"horizon-like-emission-from-curvature-bound-coherence-fields","status":"publish","type":"post","link":"https:\/\/coherencegeometry.com\/index.php\/2026\/05\/18\/horizon-like-emission-from-curvature-bound-coherence-fields\/","title":{"rendered":"Horizon-Like Emission from Curvature-Bound Coherence Fields"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>Internal ID:<\/strong> CGI-RSR-000023<br><strong>Author(s):<\/strong> Barry L. Petersen<br><strong>Document Type:<\/strong> Research Paper<br><strong>Publication Date:<\/strong> May 2026<br><strong>Original Creation Date:<\/strong> February 27, 2026<br><strong>Revised Document Date:<\/strong> May 18, 2026<br><strong>Status:<\/strong> Public<br><strong>Domains:<\/strong> Physics<br><strong>Sub-Domain:<\/strong> Cosmology, Black Holes and Horizon Structure<br><strong>Research Topics:<\/strong> Hawking Radiation, Black holes, Noether theorem<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><br>We investigate horizon-like emission from curvature-regulated coherence fields within the Coherence Geometry (CG) framework. Using a multi-phase Lagrangian that incorporates curvature stiffness and phase-locking interactions, we numerically simulate the relaxation of a confined coherence region bounded by a curvature rim. The resulting outward flux exhibits robust inverse-square scaling with boundary radius, <\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msub><mi>F<\/mi><mrow><mtext><\/mtext><mi>avg<\/mi><\/mrow><\/msub><mo>\u221d<\/mo><msubsup><mi>R<\/mi><mi>c<\/mi><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mn>2<\/mn><\/mrow><\/msubsup><mo separator=\"true\">,<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">F_{\\mathrm{avg}} \\propto R_c^{-2}, <\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div style=\"height:29px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">consistent across all simulated geometries. This scaling arises from local geometric interactions and conserved exterior flux, without invoking statistical, quantum, or thermodynamic assumptions. The results demonstrate that curvature-trapping interfaces in deterministic coherence dynamics naturally produce geometric emission with universal dilution behavior. We discuss the structural relationship between this mechanism and horizon emission phenomena in semiclassical settings.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Available Document<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>DOI:<\/strong> <code>10.5281\/zenodo.20266162<\/code><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Citation:<\/strong><br>Petersen, B. L. (2026). Horizon-Like Emission from Curvature-Bound Coherence Fields. Zenodo.&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.20266162\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.20266162<\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Representative Figure<\/h3>\n\n\n\n<div style=\"height:12px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<style>.kb-image3389_9f85c3-27.kb-image-is-ratio-size, .kb-image3389_9f85c3-27 .kb-image-is-ratio-size{max-width:506px;width:100%;}.wp-block-kadence-column > .kt-inside-inner-col > .kb-image3389_9f85c3-27.kb-image-is-ratio-size, .wp-block-kadence-column > .kt-inside-inner-col > .kb-image3389_9f85c3-27 .kb-image-is-ratio-size{align-self:unset;}.kb-image3389_9f85c3-27 figure{max-width:506px;}.kb-image3389_9f85c3-27 .image-is-svg, .kb-image3389_9f85c3-27 .image-is-svg img{width:100%;}.kb-image3389_9f85c3-27 .kb-image-has-overlay:after{opacity:0.3;border-top-left-radius:10px;border-top-right-radius:10px;border-bottom-right-radius:10px;border-bottom-left-radius:10px;}.kb-image3389_9f85c3-27 img.kb-img, .kb-image3389_9f85c3-27 .kb-img img{border-top:2px solid var(--global-palette5, #4A5568);border-right:2px solid var(--global-palette5, #4A5568);border-bottom:2px solid var(--global-palette5, #4A5568);border-left:2px solid var(--global-palette5, #4A5568);border-top-left-radius:10px;border-top-right-radius:10px;border-bottom-right-radius:10px;border-bottom-left-radius:10px;box-shadow:10px 10px 30px 0px rgba(0, 0, 0, 0.2);}@media all and (max-width: 1024px){.kb-image3389_9f85c3-27 img.kb-img, .kb-image3389_9f85c3-27 .kb-img img{border-top:2px solid var(--global-palette5, #4A5568);border-right:2px solid var(--global-palette5, #4A5568);border-bottom:2px solid var(--global-palette5, #4A5568);border-left:2px solid var(--global-palette5, #4A5568);}}@media all and (max-width: 767px){.kb-image3389_9f85c3-27 img.kb-img, .kb-image3389_9f85c3-27 .kb-img img{border-top:2px solid var(--global-palette5, #4A5568);border-right:2px solid var(--global-palette5, #4A5568);border-bottom:2px solid var(--global-palette5, #4A5568);border-left:2px solid var(--global-palette5, #4A5568);}}<\/style>\n<div class=\"wp-block-kadence-image kb-image3389_9f85c3-27\"><figure class=\"aligncenter size-medium_large\"><img loading=\"lazy\" decoding=\"async\" width=\"768\" height=\"576\" src=\"https:\/\/coherencegeometry.com\/wp-content\/uploads\/2026\/05\/fig_rim_flux_vs_radius_log-log-768x576.png\" alt=\"\" class=\"kb-img wp-image-3411\" srcset=\"https:\/\/coherencegeometry.com\/wp-content\/uploads\/2026\/05\/fig_rim_flux_vs_radius_log-log-768x576.png 768w, https:\/\/coherencegeometry.com\/wp-content\/uploads\/2026\/05\/fig_rim_flux_vs_radius_log-log-300x225.png 300w, https:\/\/coherencegeometry.com\/wp-content\/uploads\/2026\/05\/fig_rim_flux_vs_radius_log-log-1024x768.png 1024w, https:\/\/coherencegeometry.com\/wp-content\/uploads\/2026\/05\/fig_rim_flux_vs_radius_log-log-1536x1152.png 1536w, https:\/\/coherencegeometry.com\/wp-content\/uploads\/2026\/05\/fig_rim_flux_vs_radius_log-log-2048x1536.png 2048w\" sizes=\"auto, (max-width: 768px) 100vw, 768px\" \/><\/figure><\/div>\n\n\n\n<div style=\"height:11px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><em>Log\u2013log scaling of average rim power versus radius. The best-fit exponent<\/em> p = 1.99 \\( \\pm \\)<em> .04 demonstrates that the flux follows an inverse-square dependence, consistent with<\/em> <em>geometric propagation of curvature energy.<\/em><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Source Code and Supporting Materials<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Computational materials:<\/em><br>This Zenodo record includes research-artifact notebooks and data associated with<br>the numerical results in the paper. These materials are provided for inspection,<br>transparency, and reproducibility support, but are not packaged as maintained<br>software.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Files included:<\/em><br><br><strong>cg_action_flux_radial_GOLD.ipynb<\/strong><br>Research notebook implementing the radial CG action-flux simulator. This notebook generates rim-intensity \/ rim-power data for a selected curvature rim radius and saves output files and plots to a local folder. The notebook can be repeated for each radius used in the study. Generated 2D image frames are used in the paper to illustrate the radiative effect.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>rim_power_combiner.ipynb<\/strong><br>Utility notebook that combines the individual rim-power CSV files generated for each radius into the combined dataset rim_power_all.csv.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">analyze_rim_flux.ipynb<br>Analysis notebook that reads rim_power_all.csv and generates the main line and scatter plots reported in the paper, saving the resulting figures to a local folder.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>rim_power_all.csv<\/strong><br>Combined rim-power dataset used by analyze_rim_flux.ipynb. This file is included as a shortcut so that readers can reproduce the analysis plots without rerunning the full simulator for every radius.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>rim_power_output.zip<\/strong><br>Archive of the original per-radius output data collected during the study. These files can be used with rim_power_combiner.ipynb to regenerate rim_power_all.csv.<br><em><br>Workflow summary:<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>cg_action_flux_radial_GOLD.ipynb<\/strong><br>-&gt; per-radius rim-power output files and 2D emission plots<br>-&gt; <strong>rim_power_combiner.ipynb<\/strong><br>-&gt; <strong>rim_power_all.csv<\/strong><br>-&gt; <strong>analyze_rim_flux.ipynb<\/strong><br>-&gt; paper plots<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Reproducibility note:<\/em><br>The notebooks are provided as research artifacts associated with the paper, not as a maintained software package. They may require local path adjustments, environment setup, and manual selection of radius values before execution. The included <em>rim_power_all.csv<\/em> file allows the main analysis plots to be reproduced without rerunning the full simulator.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Code and data availability:<\/em><br>The Zenodo record includes the simulator notebook, combiner notebook, analysis notebook, combined rim-power dataset, and original per-radius output archive used for the figures and scaling analysis. No public technical support is implied.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary and Notes<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Scope:<\/em><br>This document should be read as a CG-native horizon-like emission study focused on geometric flux generation and inverse-square dilution. The paper does not reproduce the standard semiclassical quantum-field-theoretic derivation of Hawking radiation. Instead, it uses deterministic curvature-bound coherence dynamics to show how horizon-like interfaces can generate outward radiative flux with (R_c^{-2}) scaling.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The result is supported by a detailed energy-flux formulation, including stress-energy and Noether-current derivations, and by numerical notebooks that generate the rim-flux scaling data and time-resolved emission frames.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The included notebooks also generate time-resolved visual frames of the radiating coherence field, making the emission process inspectable as a geometric evolution rather than only as an inferred statistical or semiclassical effect.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Framework context:<br>The paper belongs to the Physics \/ Black Holes and Horizon Structure or Cosmology areas of the Coherence Geometry research corpus. It uses CG amplitude-phase field dynamics to model curvature-bound coherence regions, trapping interfaces, and outward-propagating flux.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Related Work<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Related research:<br>Petersen, B. L. (2026). Planck&#8217;s Constant as a Coherence Quantization from Phase Geometry. Zenodo. <a href=\"https:\/\/doi.org\/10.5281\/zenodo.20257619\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.20257619<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Related framework:<br>Petersen, B. L. (2026). Coherence Geometry Foundations, Part I: Orientation,<br>Closure, and Algebraic Foundations (Version 0.1). Zenodo.<br><a href=\"https:\/\/doi.org\/10.5281\/zenodo.20156532\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.20156532<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Petersen, B. L. (2026). Coherence Geometry Foundations, Part II: Physical<br>Projections (Version 0.1). Zenodo.<br><a href=\"https:\/\/doi.org\/10.5281\/zenodo.20156997\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.20156997<\/a><\/p>\n\n\n\n","protected":false},"excerpt":{"rendered":"<p>CGI-RSR-000023 | We investigate horizon-like emission from curvature-regulated coherence fields within the Coherence Geometry (CG) framework. Using a multi-phase Lagrangian that incorporates curvature stiffness and phase-locking interactions, we numerically simulate the relaxation of a confined coherence region bounded by a curvature rim.<\/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":[70,37,31,56],"tags":[],"class_list":["post-3389","post","type-post","status-publish","format-standard","hentry","category-black-holes-and-horizon-structure","category-cosmology","category-physics","category-research-papers"],"_links":{"self":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/posts\/3389","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=3389"}],"version-history":[{"count":24,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/posts\/3389\/revisions"}],"predecessor-version":[{"id":3471,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/posts\/3389\/revisions\/3471"}],"wp:attachment":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/media?parent=3389"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/categories?post=3389"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/tags?post=3389"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}