The r = 0 Hypersurface as a Coordinate Boundary: A Classical Geometric Argument from the Schwarzschild-FLRW Equivalence

This paper provides a formal geometric proof establishing the r = 0 hypersurface of the Schwarzschild interior as a classical coordinate boundary rather than a physical singularity. By exploiting the exact equivalence between the Schwarzschild interior metric and the FLRW cosmological model via the cycloidal parametrization r(η) = (r_s/2)(1 + cos η), we show that the radial acceleration at η = π (r = 0) is strictly positive (+r_s/2 > 0) and the radial velocity vanishes — the structure of a geometric turning point, not a termination. Spatial flatness (Ω_k = 0) and the Horizon problem are resolved via Israel junction conditions at r = r_s without invoking inflation. A falsifiable gravitational wave echo…