From UD Theory to Black Holes and Vacuum: A Unified Derivation of Spacetime Singularities and Quantum Vacuum

This paper derives black hole thermodynamics and vacuum structure as natural consequences of UD theory under extreme conditions from a single fundamental axiom. The axiom is based on the universe originating from the critical state U = D, and through the logical necessity of “mutual containment”, the four-aspect structure UU , UD, DD, DU is derived. Black holes are products of the extreme condensation of DD, with their thermodynamic properties derived from the UD field equations, and Hawking radiation consistent with post-Newtonian corrections. The vacuum is the ground state of UU and UD, with its expectation values determined by the four-aspect structure, naturally resolving the vacuum catastrophe. Black holes and vacuum, as the two extreme states of UD theory—extreme condensation and extreme dispersion—form a perfect symmetry.