Æther Model – Structural Cartography of Black Holes: Domains of Validity and Breakdown of Effective Descriptions

This technical report (written in Spanish) develops a structural analysis of black holes within the Æther framework, focusing on the domains of validity of effective physical descriptions rather than on the ontological content of the black hole interior. The work examines the dynamical operators governing perturbative degrees of freedom in black hole spacetimes and identifies the mathematical conditions under which standard modal and spectral descriptions—such as quasinormal modes, physical frequencies, and autosimilar scaling—remain well defined. By analyzing the hyperbolic structure of the effective operators, the report shows that extrapolations of the modal language toward regimes of increasingly high curvature generically lead to a structural breakdown of the effective description. This breakdown manifests as a degeneration of the kinetic operator and a loss of hyperbolicity, implying the collapse of the notions of mode, frequency, and particle-like excitation beyond a finite domain of validity. The result does not correspond to quantitative corrections to general relativistic predictions, nor to the introduction of new degrees of freedom or microscopic interior dynamics. Instead, it identifies a qualitative and operator-level limitation of the effective language commonly extrapolated toward the black hole interior. The analysis reframes the notion of the black hole interior as a structural boundary of physical description rather than as a dynamically accessible region. Within the Æther research program, this report constitutes a further instance of structural validation, demonstrating how the limits of physical meaning in extreme gravitational systems can be identified through internal consistency criteria rather than through model extension or ultraviolet completion.