Generalization of Rindler Potential at Cluster Scales in
  Randers-Finslerian Spacetime: a Possible Explanation of the Bullet Cluster
  1E0657-558?
  The data of the Bullet Cluster 1E0657-558 released on November 15, 2006
reveal that the strong and weak gravitational lensing convergence $\kappa$-map
has an $8\sigma$ offset from the $\Sigma$-map. The observed $\Sigma$-map is a
direct measurement of the surface mass density of the Intracluster medium(ICM)
gas. It accounts for 83% of the averaged mass-fraction of the system. This
suggests a modified gravity theory at large distances different from Newton's
inverse-square gravitational law. In this paper, as a cluster scale
generalization of Grumiller's modified gravity model (D. Grumiller, Phys. Rev.
Lett. 105, 211303 (2010)), we present a gravity model with a generalized linear
Rindler potential in Randers-Finslerian spacetime without invoking any dark
matter. The galactic limit of the model is qualitatively consistent with the
MOND and Grumiller's. It yields approximately the flatness of the rotational
velocity profile at the radial distance of several kpcs and gives the velocity
scales for spiral galaxies at which the curves become flattened. Plots of
convergence $\kappa$ for a galaxy cluster show that the peak of the
gravitational potential has chances to lie on the outskirts of the baryonic
mass center. Assuming an isotropic and isothermal ICM gas profile with
temperature $T=14.8$ keV (which is the center value given by observations), we
obtain a good match between the dynamical mass $M_\textmd{T}$ of the main
cluster given by collisionless Boltzmann equation and that given by the King
$\beta$-model. We also consider a Randers+dark matter scenario \textbf{and a
$\Lambda$-CDM model} with the NFW dark matter distribution profile. We find
that a mass ratio $\eta$ between dark matter and baryonic matter about 6 fails
to reproduce the observed convergence $\kappa$-map for the isothermal
temperature $T$ taking the observational center value.
