Galaxy rotation curves from a fourth order gravity
  While the standard and most popular explanation for the flatness of galaxy
rotation curves is dark matter, one cannot at this stage rule out an
explanation based on a modified law of gravitation, which agrees with Newtonian
gravitation on the scale of the solar system, but differs from it on larger
length scales. Examples include Modfied Newtonian Dynamics [MOND] and
Scalar-Tensor-Vector Gravity [STVG]. Here we report on a fourth order
modification of the Poisson equation which yields the same Yukawa type
modification of Newtonian gravity as STVG, and which can explain flat galaxy
rotation curves for a large sample of galaxies, once specific values for two
parameters have been chosen. We speculate on two possible origins for this
modified Poisson equation: first, a possible fourth order modification of
general relativity, and second, quadrupole gravitational polarization induced
on a galaxy because of the pull of neighbouring galaxies.
