Finite-Relaxation Geometry (FRG): An Effective Dynamical Extension of General Relativity

We propose Finite-Relaxation Geometry (FRG) as an effective dynamical framework in which spacetime geometry possesses a finite relaxation time toward its Einstein-equilibrium configuration. While preserving the Einstein field equations in their standard form, FRG introduces a phenomenological timescale governing the dynamical adjustment of the metric following curvature perturbations. The framework does not modify the local structure of General Relativity, introduces no additional fields or particles, and remains fully covariant in the equilibrium limit. We demonstrate that a finite geometric relaxation time naturally leads to long-lived nonequilibrium curvature contributions, interpretable as geometric memory. FRG is shown to be consistent with relativistic principles and provides a well-defined foundation for further astrophysical and cosmological applications.