Dark Matter as Non-Equilibrium Virial Geometry

Abstract

The dark-matter problem is usually interpreted as evidence for unseen mass. This paper develops a different closure: the missing term may be the finite relaxation of spacetime geometry itself. Starting from the full time-dependent Virial Theorem, the normally discarded non-equilibrium term is retained and interpreted as the observable memory of a gravitational field still reorganizing toward its baryonic sources. This defines a local environmental clock, tau_eff, not as a universal fitted constant but as a measurable relaxation time.Using SPARC and THINGS rotation-curve data, the clock orders galactic environments in the predicted direction: dynamically fast, baryon-dominated regions relax quickly, while weakly driven outer regions retain longer memory. With the clock fixed, the same framework is tested against apparent halo endpoints, ultra-diffuse suppressed-response systems, and merger-lag estimates without fitting halo masses or concentrations. A separate channel test shows that orbital dynamics remains on the scalar branch, while weak lensing reads a fixed optical projection, A_lens = 19/15, matching the combined KiDS+GAMA+HSC residual amplitude.The result is a unified virial-geometric interpretation of dark-sector phenomenology: rotation curves, apparent halos, merger lags, and enhanced lensing amplitudes arise as different observational readouts of one residual weak-field geometry, rather than as separate evidence requiring a new particle species.