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The strong equivalence principle (SEP) distinguishes General Relativity fromother viable theories of gravity. The SEP demands that the internal dynamics ofa self-gravitating system under free-fall in an external gravitational fieldshould not depend on the external field strength. We test the SEP byinvestigating the external field effect (EFE) in Milgromian dynamics (MOND),proposed as an alternative to dark matter in interpreting galactic kinematics.We report a detection of this EFE using galaxies from the Spitzer Photometryand Accurate Rotation Curves (SPARC) sample together with estimates of thelarge-scale external gravitational field from an all-sky galaxy catalog. Ourdetection is threefold: (1) the EFE is individually detected at $8\sigma$ to$11\sigma$ in "golden" galaxies subjected to exceptionally strong externalfields, while it is not detected in exceptionally isolated galaxies, (2) theEFE is statistically detected at more than $4\sigma$ from a blind test of 153SPARC rotating galaxies, giving a mean value of the external field consistentwith an independent estimate from the galaxies' environments, and (3) we detecta systematic downward trend in the weak gravity part of the radial accelerationrelation at the right acceleration predicted by the EFE of the MOND modifiedgravity. Tidal effects from neighboring galaxies in the $\Lambda$CDM contextare not strong enough to explain these phenomena. They are not predicted byexisting $\Lambda$CDM models of galaxy formation and evolution, adding a newsmall-scale challenge to the $\Lambda$CDM paradigm. Our results point to abreakdown of the SEP, supporting modified gravity theories beyond GeneralRelativity.

Testing the Strong Equivalence Principle: Detection of the External Field Effect in Rotationally Supported Galaxies