Wide binaries as a critical test for Gravity theories
  Assuming Newton's gravity and GR to be valid at all scales leads to the dark
matter hypothesis as a requirement demanded by the observed dynamics and
measured baryonic content at galactic and extragalactic scales. Alternatively,
modified gravity scenarios where a change of regime appears at acceleration
scales $a<a_{0}$ have been proposed. This modified regime at $a<a_{0}$ will
generically be characterised by equilibrium velocities which become independent
of distance. Here we identify a critical test in this debate and we propose its
application to samples of wide binary stars. Since for $1 M_{\odot}$ systems
the acceleration drops below $a_{0}$ at scales of around 7000 AU, a statistical
survey of wide binaries with relative velocities and separations reaching
$10^{4}$ AU and beyond should prove useful to the above debate. We apply the
proposed test to the best currently available data. Results show a constant
upper limit to the relative velocities in wide binaries which is independent of
separation for over three orders of magnitude, in analogy with galactic flat
rotation curves in the same $a<a_{0}$ acceleration regime. Our results are
suggestive of a breakdown of Kepler's third law beyond $a \approx a_{0}$
scales, in accordance with generic predictions of modified gravity theories
designed not to require any dark matter at galactic scales and beyond.
