Elongated Gravity Sources as an Analytical Limit for Flat Galaxy
  Rotation Curves
  The flattening of spiral-galaxy rotation curves is unnatural in view of the
expectations from Kepler's third law and a central mass. It is interesting,
however, that the radius-independence velocity is what one expects in one less
dimension. In our three-dimensional space, the rotation curve is natural if,
outside the galaxy's center, the gravitational potential corresponds to that of
a very prolate ellipsoid, filament, string, or otherwise cylindrical structure
perpendicular to the galactic plane. While there is observational evidence (and
numerical simulations) for filamentary structure at large scales, this has not
been discussed at scales commensurable with galactic sizes. If, nevertheless,
the hypothesis is tentatively adopted, the scaling exponent of the baryonic
Tully--Fisher relation due to accretion of visible matter by the halo comes out
to reasonably be 4. At a minimum, this analytical limit would suggest that
simulations yielding prolate haloes would provide a better overall fit to
small-scale galaxy data.
