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Global Transmission Universality and Local Critical Diversity in a Six-Throat Geometry

Year: 2026
Type: article
Abstract: We construct a static, spherically symmetric, ultrastatic geometry containing exactly six regular equal-radius throats along a single proper-radial coordinate and use it as a controlled analytic setting for studying the relation between local critical structure and global null transmission. The areal-radius profile has six simple minima at s=±l, ±2l, ±3l all with A_min=a>0, and two proper-distance-unbounded ends. The Ricci scalar, quadratic Ricci invariant, and Kretschmann scalar remain finite at every finite proper-radial coordinate and decay toward both ends. Null geodesics exhibit a single end-to-end transmission boundary, b_crit=a: trajectories with |b|a forbids complete transmission. Despite this global universality, the six throats are locally optically inequivalent. Their leading near-critical logarithmic angular responses form three reflection-related classes with coefficients C1=1/48, C2=1/60, and C3=1/240. We further show that this global-local separation persists under a controlled class of sufficiently small smooth profile perturbations preserving the common positive-radius floor: the throat positions may shift and reflection symmetry may be broken while six simple equal-radius minima and the common threshold survive, whereas the local critical coefficients remain deformation-sensitive. Independent symbolic, tensor-based, and numerical reconstructions reproduce the principal geometric and optical results, with representative numerical estimates of the logarithmic coefficients agreeing with the analytic values at sub-percent level. The construction therefore provides a higher-complexity analytic benchmark demonstrating that local critical multiplicity need not map one-to-one onto global transmission multiplicity
DOI: 10.5281/zenodo.22207681
Language: English
Open Access status: green
OpenAlex ID: W7204778291
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