Galaxies Rotation Curves in the Grumiller's Modified Gravity
  The effective potential in the Grumiller's modified gravity [D. Grumiller,
Phys. Rev. Lett {\bf 105}, 211303 (2010)] includes the Newtonian potential and
a Rindler term. The fitting to the rotation curve data of eight galaxies
suggests a universal Rindler acceleration $a\approx 0.30\times 10^{-10}$ m
s$^{-2}$. We do a two-parameter fit first, with the mass-to-light ratio
($\Upsilon_*$) and the Rindler acceleration ($a$) as free parameters. It is
found that the data of six out of the eight galaxies fit well with the
prediction of theory in the range $0\lesssim r \lesssim 40$ kpc, although the
theoretical curves show a tendency of arising beyond this range. The Rindler
accelerations of the six well-fitted galaxies have the same magnitude, with an
average value $\bar{a}\approx0.30\times 10^{-10}$ m s$^{-2}$. Inspired by this
fact, we then carry out a one-parameter ($\Upsilon_*$) fit to the six galaxies,
with $a$ fixed at $\bar{a}$, and find that the theory can still reproduce the
observation. The value of Rindler acceleration we get here is a quarter of that
of Milgrom's MOND. For the rest two galaxies, NGC5055 and DDO154, the fitting
results are significantly improved if the photometric scale length ($h$) is
included as another free parameter.
