A Certification-Based Formalism for the Event Horizon Boundary

Abstract

The event horizon is traditionally defined as a geometric surface beyond which causal signalscannot escape. In this note we propose an alternative, purely structural vocabulary for describingthe same object. We introduce a certification framework, in which a carrier domain C is equippedwith an admissibility map assigning to each configuration a set of certified continuations. Withinthis formalism, the event horizon can be characterized as the boundary ∂C C across which thecertified multiplicity collapses from more than one admissible continuation to exactly one. Weshow this characterization is consistent with the classical Schwarzschild horizon condition gtt =0, and we discuss standard geometric horizon diagnostics (null trapping, causal disconnection,the Schwarzschild radius) as they appear under this vocabulary.We emphasize that this is a proposed descriptive formalism, not a derivation: the certificationmap C is not, at present, independently computable from first principles of general relativity,and the framework’s value is organizational rather than predictive. We state explicitly whatwould be required to upgrade it to a genuinely explanatory theory.