A Mathematical View on the Coordinate Distortion Induced by Gravitational Waves

We develop a theoretical framework to analyze how coordinate systems deform under the influence of gravitational waves. This model treats coordinates as nodes in a discrete spatial graph, with inter-node distances perturbed by time-varying distortions due to passing waves. A direct proportionality is proposed between the distortion and the energy density of the wave, analogous to strain measured in interferometric detectors. We also relate this to the geodesic deviation equation from general relativity and propose directions for extending the model with continuous differential geometry and perturbation theory.