The Spacetime Resonance Theorem and the Origin of Dark Mass

This work applies a well-known idea from acoustics and optics—multiple scattering in a medium—to gravity itself. In linearised general relativity the gravitational field is determined by a retarded Green function, but in most applications its “causal tail’’ (the part inside the light cone) is discarded. When this tail is kept and combined with the linear damped-oscillator susceptibility we introduce for baryonic matter (mathematically identical to the response used in acoustical and optical scattering theory) spacetime behaves as an effective transport medium for weak curvature waves. From this simple starting point we derive a single theorem—the Spacetime Resonance Theorem—showing how coherent, time-varying baryonic motion generates a small resonant curvature field. Multiple gravitational scattering causes part of this oscillatory field to accumulate as a slow, cycle-averaged component. This stored curvature energy behaves exactly like an effective dark-mass density. The resulting framework naturally reproduces the observed dark-mass profiles of spiral galaxies, ellipticals, clusters, and filaments; predicts “local silence’’ and “homogeneous silence’’ (matching the Bullet Cluster and the CMB); and remains fully consistent with standard GR. No new particles or modifications of gravity are introduced: dark-mass behaviour emerges from the resonant, multiple-scattering response of baryonic structure within ordinary weak-field GR.