Viscoelastic General Relativity: Spacetime with Memory as an Alternative to Dark Matter

This work formulates Viscoelastic General Relativity (VGR), a phenomenological extension of General Relativity in which spacetime responds to stress energy with a finite relaxation time. The theory introduces a covariant spacetime memory tensor governed by a causal constitutive law, without invoking new matter fields or particle dark matter. The framework preserves local tests of gravity and reduces exactly to General Relativity in the fast response limit. At astrophysical scales, delayed curvature response leads to effective gravitational enhancements in slowly evolving systems and to transient offsets between baryonic matter and gravitational lensing in dynamically disturbed systems, such as merging galaxy clusters. A weak field, quasistatic limit is derived, showing how the memory contribution enters the Poisson equation and yields an emergent acceleration scale without postulating a universal dark matter density. The work is intended as a conceptual and mathematical foundation for further analytical and observational testing.