Geometric Extension of the Dual-Field Interface Model: Modified Metrics and Stable Black Hole Remnants (Version 1.0)

This paper presents the Geometric Extension of the Dual-Field Interface Model (DFIM), bridging the gap between the model's mechanical framework (based on quantum tunneling and surface tension) and the geometric language of General Relativity. While previous iterations (DFIM v3.3) described black hole stability via mechanical "weld stiffness" and Landau-Zener transitions, this paper derives the modified Schwarzschild metric that produces these results geometrically. We introduce a "tidal charge-like" parameter, β, which represents the repulsive tension of the Negative Energy field acting across the spacetime interface. Key theoretical advancements: The Modified Metric: We derive a metric f(r)=1−rs/r+β/r2, where β arises from inter-field tension rather than electromagnetic charge. This creates a "blunted" gravitational potential that prevents singularities. Geometric Resolution to Evaporation: We show that the adapted Hawking temperature does not diverge to infinity. Instead, it vanishes at the extremal limit (rs2=4β), effectively creating a "SCRAM" mechanism that halts evaporation. Stable Remnants (Dark Matter): The model mathematically predicts that black holes stabilize at a non-zero minimum mass (Mmin≈10−5M⊙ in loose vacuum regimes), providing a geometric proof for the Dark Matter candidates predicted in the main thesis. Braneworld Connection: The paper establishes formal links to Randall-Sundrum braneworld gravity and "tidal charge" models (e.g., Dadhich et al., 2000), offering a unified framework for information preservation and energy balance. This paper serves as the geometric companion to the main DFIM thesis and the EM Extension, completing the trilogy by integrating the theory into curved spacetime. Keywords Dual-Field Interface Model, DFIM, General Relativity, Modified Schwarzschild Metric, Black Hole Remnants, Dark Matter, Information Paradox, Braneworld Gravity, Tidal Charge, Hawking Radiation.