BH-WW: The Thermodynamic and Topological Cosmic Cauldron: Gravitational-Cosmological Time Equivalence, Transient Klein Throats, Geothermal/Astrophysical Heat Traps, and 4-Dimensional Phase Circulation

Standard cosmological models condemn the metric expansion of the universe, gravitational singularities, and thermodynamic evolution to an open-ended, irreversible, and entropic heat death scenario. Similarly, standard astrophysics and geophysics attempt to account for the core temperatures of celestial bodies (the Earth’s core heat, Jupiter and Saturn radiating more energy than they receive from the Sun, Enceladus’s geysers) via radioactive decay and primordial accretion heat, yet they fail to close the measured massive heat deficits with satisfactory physical causality. This work (the Black Hole–White Wall / BH-WW Model) formulates the universe as a frictionless, 4-dimensional closed “spherical pot/cauldron” model in which bubbles boiling and evaporating from the inside out, and condensing and contracting back inward at the boundary, are interconnected through dynamic Klein vents. The founding pillar of the model is built upon a unified time axiom demonstrating that gravitational time dilation, curvature geodesic delay, and cosmological expansion time delay are identical within the horizon of the operational radar distance (d = 2 1 c∆t). From the standpoint of an observer’s detector, the event horizon of a local black hole (r → r s ) and the outer cosmological boundary located 14 billion light-years away (t → 0) constitute a single topological conjugate exhibiting the exact same signature of infinite delay (∆t → ∞) and infinite redshift (z → ∞). The blueshift of light approaching mass and the dilation of clocks are direct consequences of an “elongated and narrow axial cylinder” geometry, where the temporal depth extends in response to the compressed spatial cross-section of spacetime; photons compress their frequency to preserve their invariant speed (c). Just as light propagating across free space converges toward the center of mass, thermal photons within a massive body scatter in all directions while exhibiting an asymmetric and dominant inward bias toward the center due to curvature geodesics; this inevitably makes the interior of celestial bodies hotter than their exterior. If the mass remains below the critical black hole threshold (planets and moons), this blueshifted, inwardly scattering energy seeks a Klein drainage vent at the center; because the vent cannot open, the energy remains trapped within the core, manifesting as continuous internal pressure and thermal heat. This provides a purely mechanical solution to the unexplained heat budget deficits in geophysics. In black holes, the critical mass threshold is exceeded, transient Klein throats open, and the 4-volume evacuates to the outer boundary. Metric expansion (a(t)) is the macroscopic evacuation of the temporal fibers of trillions of constituent particles into spatial dimensions. The system embodies Wheeler’s geometrodynamic loop through an explicit light-mass reciprocity, forming a boundaryless, lossless, infinite thermodynamic and geometric cycle founded upon 4-dimensional incompressible volume conservation (Ω 4 = ∆V 3 · c∆τ = constant).