General Relativity and the Identity of Spacetime

General relativity fixes how a geometry evolves; it does not, from within, say when a later geometry is the same spacetime, when the energy of a bounded region is well-posed, which of several “horizons” bounds a system, or when a continuation past a singularity continues the same universe. These are not gaps in the field equations; they are identity and system-specification questions the theory presupposes whenever it speaks of “the black hole,” “the universe,” or “the energy of the system.” The paper shows that general relativity already contains the mathematical ingredients — the maximal globally hyperbolic development, isometry, Geroch’s topology theorem, the quasi-local energy constructions, the horizon taxonomy — and that La Profilée supplies the explicit identity/admissibility criterion and the verdict discipline (existence Q1 kept strictly before identity Q2), so that the combination yields determinate classifications the theory alone leaves open. The central positive result, for stages in the globally hyperbolic continuation structure: while a spacetime remains globally hyperbolic, it is the same spacetime through arbitrarily strong geometric change — an expanding universe is, under this criterion, the same universe. No equation is modified and no value is delivered.