Dual-Horizon Metric, Topological Drainage, and Modified Field Equations in the Black Hole–White Wall (BH-WW) Cyclic Non-Expanding Cosmological Model Hypothesis

The standard cosmological model (ΛCDM) and classical General Relativity lose their mathematical validity at two fundamental boundaries: the local physical singularities within black holes and the temporal initial Big Bang singularity (t = 0). This work postulates that spacetime does not undergo metric expansion; rather, the universe is a 4-dimensional, compact, non-orientable Klein manifold bounded internally by N BH ∼ 10 20 local black hole throats (drainage valves) and externally by a spherical boundary shell (White Wall). Cosmological redshift is not a kinetic signature of spatial expansion, but the direct consequence of the gravitational potential well (N → 0 symmetry) established on the boundary shell by mass drained into the fourth dimension via black hole throats. The singularities of classical General Relativity are eliminated via the regularized throat coordinate r 2 = r 0 2 + l 2 and Klein a topological stress tensor H µν . The observational absence of isolated, galaxy-depleted 10 11 M ⊙ supermassive black holes and their systematic decay toward the 10 9 M ⊙ threshold are modeled through dynamic drainage coupled with orbital unbinding. The metric tensor, energy-momentum continuity, and modified Einstein field equations are analytically derived.