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

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.