Emergent General Relativity: Deriving the Schwarzschild Metric from a Torsional Harmonic Lattice

This paper derives General Relativity and the Schwarzschild metric from the microscopic dynamics of a discrete harmonic vacuum lattice, positing that gravity is an emergent variation in vacuum impedance rather than a fundamental force. Using a minimal lattice action principle and the axiom of vacuum impedance conservation, the study demonstrates that mass acts as a topological defect creating radial tension, which modifies local lattice properties. The model successfully reproduces the Schwarzschild metric, gravitational light deflection, and Mercury's perihelion precession ($43"/century$) without free parameters. Furthermore, it interprets the event horizon as a phase transition to a saturated coherence state and calculates a value for the cosmological constant (Dark Energy) within two orders of magnitude of observation based on lattice zero-point energy. Emergent Gravity, Schwarzschild Metric, Vacuum Impedance, Harmonic Vacuum Lattice, General Relativity. Perihelion Precession, Event Horizon, Dark Energy, Topological Defects, Light Deflection, Lattice Dynamics, Quantum Gravity, Zero-Point Energy.