Intercluster filaments negligibly contribute to the weak lensing signal in
general relativity (GR), $\gamma_{N}\sim 10^{-4}-10^{-3}$. In the context of
relativistic modified Newtonian dynamics (MOND) introduced by Bekenstein,
however, a single filament inclined by $\approx 45^\circ$ from the line of
sight can cause substantial distortion of background sources pointing towards
the filament's axis ($\kappa=\gamma=(1-A^{-1})/2\sim 0.01$); this is rigorous
for infinitely long uniform filaments, but also qualitatively true for short
filaments ($\sim 30$Mpc), and even in regions where the projected matter
density of the filament is equal to zero. Since galaxies and galaxy clusters
are generally embedded in filaments or are projected on such structures, this
contribution complicates the interpretation of the weak lensing shear map in
the context of MOND. While our analysis is of mainly theoretical interest
providing order-of-magnitude estimates only, it seems safe to conclude that
when modeling systems with anomalous weak lensing signals, e.g. the "bullet
cluster" of Clowe et al., the "cosmic train wreck" of Abell 520 from Mahdavi et
al., and the "dark clusters" of Erben et al., filamentary structures might
contribute in a significant and likely complex fashion. On the other hand, our
predictions of a (conceptual) difference in the weak lensing signal could, in
principle, be used to falsify MOND/TeVeS and its variations.Comment: 11 pages, 6 figures, published versio