Testing the MOND Paradigm of Modified Dynamics with Galaxy-Galaxy Gravitational Lensing

The MOND paradigm of modified dynamics predicts that the asymptotic gravitational potential of an isolated, bounded (baryonic) mass, M, is (r) = (MGa₀) ^1/2ln (r). Relativistic MOND theories predict that the lensing effects of M are dictated by (r) as general-relativity lensing is dictated by the Newtonian potential. Thus MOND predicts that the asymptotic Newtonian potential deduced from galaxy-galaxy gravitational lensing will have (1) a logarithmic r dependence, and (2) a normalization (parametrized standardly as 2^2) that depends only on M: = (MGa₀/4) ^1/4. I compare these predictions with recent results of galaxy-galaxy lensing, and find agreement on all counts. For the ``blue''-lenses subsample (``spiral'' galaxies) MOND reproduces the observations well with an r^'-band M/Lₑ^{'} (1--3) (M/L) _, and for ``red'' lenses (``elliptical'' galaxies) with M/Lₑ^{'} (3--6) (M/L) _, both consistent with baryons only. In contradistinction, Newtonian analysis requires, typically, M/Lₑ^{'}130 (M/L) _, bespeaking a mass discrepancy of a factor 40. Compared with the staple, rotation-curve tests, MOND is here tested in a wider population of galaxies, through a different phenomenon, using relativistic test objects, and is probed to several-times-lower accelerations--as low as a few percent of a₀.