Gravitational lensing and modified Newtonian dynamics

Gravitational lensing is most often used as a tool to investigate the distribution of (dark) matter in the universe, but, if the mass distribution is known a priori, it becomes, at least in principle, a powerful probe of gravity itself. Lensing observations are a more powerful tool than dynamical measurements because they allow measurements of the gravitational field far away from visible matter. For example, modified Newtonian dynamics (MOND) has no relativistic extension, and so makes no firm lensing predictions, but galaxy-galaxy lensing data can be used to empirically constrain the deflection law of a MONDian point-mass. The implied MONDian lensing formalism is consistent with general relativity, in so far as the deflection experienced by a photon is twice that experienced by a massive particle moving at the speed of light. With the deflection law in place and no invisible matter, MOND can be tested wherever lensing is observed.