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The data of the Bullet Cluster 1E0657-558 released on November 15, 2006reveal that the strong and weak gravitational lensing convergence $\kappa$-maphas an $8\sigma$ offset from the $\Sigma$-map. The observed $\Sigma$-map is adirect measurement of the surface mass density of the Intracluster medium(ICM)gas. It accounts for 83% of the averaged mass-fraction of the system. Thissuggests a modified gravity theory at large distances different from Newton'sinverse-square gravitational law. In this paper, as a cluster scalegeneralization of Grumiller's modified gravity model (D. Grumiller, Phys. Rev.Lett. 105, 211303 (2010)), we present a gravity model with a generalized linearRindler potential in Randers-Finslerian spacetime without invoking any darkmatter. The galactic limit of the model is qualitatively consistent with theMOND and Grumiller's. It yields approximately the flatness of the rotationalvelocity profile at the radial distance of several kpcs and gives the velocityscales for spiral galaxies at which the curves become flattened. Plots ofconvergence $\kappa$ for a galaxy cluster show that the peak of thegravitational potential has chances to lie on the outskirts of the baryonicmass center. Assuming an isotropic and isothermal ICM gas profile withtemperature $T=14.8$ keV (which is the center value given by observations), weobtain a good match between the dynamical mass $M_\textmd{T}$ of the maincluster 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 findthat a mass ratio $\eta$ between dark matter and baryonic matter about 6 failsto reproduce the observed convergence $\kappa$-map for the isothermaltemperature $T$ taking the observational center value.

Generalization of Rindler Potential at Cluster Scales in Randers-Finslerian Spacetime: a Possible Explanation of the Bullet Cluster 1E0657-558?