A Non-Minkowskian Gedankenexperiment in Klein Spacetime: Painlev´e–Gullstrand River Kinematics, Null-Interval Annihilation, and the Horizon–Boundary Identity in the BH-WW Model

Standard relativistic cosmology rests upon pseudo-Riemannian geometries where local spacetime intervals are decomposed along mutually orthogonal timelike and spacelike coordinate axes (g tr = 0). In regions where the gravitational gradient steepens, this orthogonality construct produces coordinate artifacts that obscure the kinematics of physical flow. In this study, instead of the static Schwarzschild metric, the Painlev´e–Gullstrand (PG) river metric (dr ∥ c dt), in which space and time flow parallel along the radial axis, is placed at the center of analysis. A closed gedankenexperiment is formulated across a cosmological outer boundary (D), galactic free-field stations (A, B), and a boundary station (C) suspended at the exact ϵ → 0 margin of the event horizon of a supermassive black hole. While clocks in the outer flat region record a cosmological duration of 13.8 billion years, it is mathematically demonstrated that the local proper time of the station at the horizon boundary collapses strictly to zero (lim ϵ→0 ∆τ C = 0). Furthermore, in two-way routes where the signal is reflected by a mirror across the galactic disk, it is proven that path length does not alter this zero-time condition. This establishes that the operational metric interval between the outer boundary of the universe (the Big Bang / White Wall boundary) and the event horizon of the black hole vanishes identically (ds 2 → 0). From this, it is shown that space-time is not an Euclidean or flat Minkowski manifold; according to this model, the universe possesses the topography of a massive, multi-throated, and inside-out-folded Klein bottle directly connected to its own outer boundary (the White Wall boundary) via approximately 2 × 10 12 × 10 8 ≈ 2 × 10 20 black hole throats contained within it.