Galaxy Rotation Curves and the Radial Acceleration Relation in an Effective Viscoelastic Spacetime Framework

This work presents an effective viscoelastic framework for galactic dynamics, 
in which the observed radial acceleration relation (RAR) emerges as a quasi-steady 
outcome of a delayed gravitational response.

The model introduces a cosmologically motivated relaxation timescale (τ ∝ H⁻¹), 
leading to an emergent acceleration scale a0 ~ cH. 

Within this framework, galaxy rotation curves, the RAR, and the baryonic 
Tully–Fisher relation are reproduced without invoking particle dark matter 
or modifying general relativity at a fundamental level.

In addition, a dimensionless memory parameter (τ / t_dyn) provides a natural 
interpretation of the observed scatter in the RAR.

This version corresponds to a revised and clarified presentation of the 
dynamical framework.

This work presents the Effective Viscoelastic Model (EVM), a theoretical framework addressing galactic-scale gravitational anomalies without invoking dark matter. The central proposition is that the gravitational field responds to baryonic sources in a delayed, memory-like fashion — analogous to viscoelastic materials that retain stress history. Under this interpretation, what is conventionally attributed to dark matter halos may instead reflect the temporal structure of gravity itself: baryons inscribe gravitational memory into spacetime, and that memory manifests as the observed excess acceleration. The model derives a characteristic acceleration scale a₀ from fundamental constants (a₀ = κ·c·H₀/2π, κ = √3/2), connects naturally to the Radial Acceleration Relation, and offers falsifiable predictions for JWST-era observations. Maintained by Chang-Sik Kim, Korean Physical Society member. ORCID: 0009-0000-0601-5113.