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Chapter 22: Singularities & Condensates (Extremes)

22.2 Event Horizon & Evaporation​

Classical General Relativity characterizes the event horizon as a geometric surface of no return. Quantum Braid Dynamics reinterprets this boundary as a computational phase boundary, explaining Hawking radiation not as spontaneous particle pair-creation in empty space, but as unitary, boundary-spanning topological swaps.

22.2.1 Definition: Desynchronization Boundary​

Characterization of Event Horizons as Phase Boundaries of Infinite Error-Correction Latency
  • Lapse Dilation Divergence: Near the horizon, the Lapse function N(x)N(x) falls toward zero relative to the external asymptotic flat space (§14.1).
  • QECC Latency: The Quantum Error Correction Code (QECC) stabilizing the manifold requires a finite number of logical ticks Δtcorr\Delta t_{corr} to complete a full correction cycle.
  • Desynchronization Surface: The physical time required for an error correction cycle diverges as Δτ=N(x)Δtcorr→∞\Delta \tau = N(x) \Delta t_{corr} \to \infty. This defines the Event Horizon not as a physical membrane, but as a computational phase boundary of infinite error-correction latency where the interior causally desynchronizes from the exterior.

22.2.2 Theorem: Unitary Evaporation​

Preservation of Black Hole Unitarity via Boundary-Mediated Topological Swaps
  • Boundary Spanning Moves: Although the interior is desynchronized, non-local graph rewrite operations R\mathcal{R} can span across the horizon boundary, connecting nodes just inside the desynchronization limit with nodes just outside.
  • Topological Swaps: These rewrites represent boundary-mediated tunneling events that swap high-entropy braid configurations from the frozen core with simple vacuum cycles from the exterior.
  • Unitary Radiation: Because these swaps are governed by strictly unitary rewrite operators, the emitted radiation is quantum-entangled with the core state, carrying information out and ensuring that the evaporation process is completely unitary.

22.2.3 Proof: Unitary Evaporation​

Verification of Black Hole Unitarity through Integration of Entanglement Page Curves
  • Tunneling Rate Evaluation: The proof calculates the non-perturbative transition probability Γ∝e−S\Gamma \propto e^{-S} of the boundary topological swap operators.
  • Page Curve Derivation: By integrating the entanglement entropy of the emitted radiation over the lifetime of the core, it shows that the entropy strictly follows the Page Curve, returning to zero at complete evaporation without firewall creation, proving global unitarity.