The Event Horizon as a Lattice Fracture Surface: Resolving the Information Paradox via Stiffness Saturation

Paper XII: The Event Horizon Fracture Title: Paper XII: The Event Horizon as a Lattice Fracture Surface - Resolving the Information Paradox via Stiffness Saturation Author: Bijan Pedram Description: General Relativity predicts that gravitational collapse leads to a singularity—a point of infinite density where the laws of physics break down. In this study, we demonstrate that such singularities are geometrically impossible in a discrete, quantized spacetime. Building on the hypothesis of a Vacuum Jamming Transition, we model the gravitational collapse of a massive star as a stress test of the vacuum lattice. We derive the Stiffness-Corrected Einstein Field Equations, showing that as local energy density approaches the Planck limit, the vacuum bulk modulus diverges and the effective gravitational coupling vanishes. We propose that the Event Horizon represents a Lattice Fracture Surface—a critical phase boundary where the vacuum loses its causal connectivity due to stiffness saturation. Consequently, the interior of the black hole becomes a topologically disconnected region, forcing all infalling quantum information to be encoded on the surface boundary. This provides a mechanical derivation of the Bekenstein-Hawking Area Law. The Holographic Principle is thus revealed not as an abstract duality, but as a physical consequence of information exclusion from the fractured volume. We conclude with a falsifiable prediction of Gravitational Wave Echoes in binary merger ringdowns. These echoes arise because the fracture surface acts as a rigid boundary, creating a resonant cavity with the exterior potential barrier. We demonstrate that these unique post-merger signals should be detectable by next-generation interferometers.