Spacetime Imprint Theory: A Phenomenological Extension of General Relativity with Finite Memory

Spacetime Imprint Theory: A Phenomenological Extension of General Relativity with Finite Memory Description:This work presents Spacetime Imprint Theory (SIT), a phenomenological extension of General Relativity in which spacetime is modeled as a physical medium endowed with finite geometric memory and a characteristic relaxation time. Unlike the instantaneous response assumed in classical General Relativity, the proposed framework allows spacetime curvature to retain a cumulative imprint of past mass–energy configurations, which gradually decays over time. The theory introduces five fundamental laws governing the formation, persistence, superposition, decay, and dynamical role of spacetime imprints. Within this framework, long-term gravitational phenomena—such as flat galactic rotation curves, the stability of orbital systems, and large-scale cosmic dynamics—are explained without invoking Dark Matter or Dark Energy as independent physical entities. A scalar imprint formulation is proposed as an effective description of spacetime memory, recovering standard General Relativity in the limit of vanishing relaxation time. The theory yields falsifiable observational predictions, including a measurable gravitational lensing lag in merging galaxy clusters, imprint-dependent galactic dynamics, and mass-threshold effects in orbital stability. This preprint is intended as a theoretical and phenomenological contribution to gravitational physics and cosmology, offering a unified geometric interpretation of the apparent dark sector while remaining consistent with known relativistic limits. Future work will focus on tensorial generalizations and numerical simulations for comparison with weak-lensing and large-scale structure surveys. Keywords:Spacetime Memory, Modified Gravity, General Relativity Extension, Galactic Rotation, Gravitational Lensing, Cosmology, Dark Matter Alternative, Dark Energy Alternative