The phenomenology of the external field effect in cold dark matter models

In general relativity (GR), the internal dynamics of a self-gravitating system under free-fall in an external gravitational field should not depend on strength. Recent work has claimed statistical detection `external effect' (EFE) using galaxy rotation curve data. We show that large uncertainties analyses and inaccuracies published simulation-based estimates compromise significance EFE detection. further analytically qualitatively similar signal is, fact, expected $\Lambda$-cold dark matter ($\Lambda$CDM) universe without any violation strong equivalence principle. Rather, such arises simply because inherent correlations between clustering strength intrinsic properties. explicitly demonstrate effect baryonified mock catalog $\Lambda$CDM universe. Although EFE-like is not, by itself, evidence for physics beyond GR, our shows $\textit{sign}$ correlation shape radial acceleration relation can be used to probe new physics: e.g., MOND, predicted sign opposite mocks.