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Friedrichs Realization and Optical Completeness for the Static Metric Associated with the Principal Eigenfunction

Year: 2026

Type: preprint

Abstract: We study the static Lorentzian metric built from the principal Dirichlet eigenfunction psi and the Friedrichs realization of the associated optical wave form. We prove constant scalar curvature, optical completeness, infinite optical volume, and a trivial kernel. The record contains the English version (main file), a faithful Portuguese version, and the supplementary archive (TeX, verification code, Lean/AXLE). Paper 1 of 3 on the spectrum of static optical metrics.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.24118829

Author: de Melo, Fábio Dayan Soares

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7225743703

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