Temporal Reconstruction of Gravitational Geometry in Dissociative Galaxy Cluster Mergers

This work investigates the temporal behavior of gravitational geometry in dissociative galaxy cluster mergers. Using a set of well-studied systems with independently constrained merger timing, we show that the observed spatial offset between the gravitational lensing signal and the X-ray emitting intracluster gas exhibits a systematic dependence on the time elapsed since core passage. Clusters observed shortly after merger display large lensing–gas separations, while systems observed at later evolutionary stages show progressively reduced offsets. This empirical trend indicates that gravitational geometry does not reorganize instantaneously following violent dynamical perturbations, but instead undergoes a finite temporal reconstruction. To describe this behavior, we introduce a minimal phenomenological equation governing the relaxation of gravitational geometry toward the evolving baryonic configuration. The formulation involves no additional forces, fields, or dark matter components, and does not modify the equations of general relativity. Instead, geometry is treated as a global structure whose realization depends on the coherence state of the system. By combining observational measurements of lensing–gas offsets with independent estimates of the time since core passage, we constrain an effective reconstruction timescale of order 0.7–1.0 Gyr. This timescale is comparable to known dynamical relaxation and turbulence-decay times in the intracluster medium, suggesting a direct connection between dynamical coherence and the realization of gravitational geometry. The results provide empirical evidence that gravitational geometry possesses a measurable temporal structure and motivate a reinterpretation of cluster lensing phenomena in strongly non-equilibrium regimes. The framework yields testable predictions for the evolution of lensing behavior across merger stages and offers a complementary perspective on gravitational phenomena without invoking additional matter components.