Finslerian MOND vs. observations of Bullet Cluster 1E0657-558
  It is known that theory of MOND with spherical symmetry cannot account for
the convergence $\kappa$-map of Bullet Cluster 1E0657-558. In this paper, we
try to set up a Finslerian MOND, a generalization of MOND in Finsler spacetime.
We use $Ric=0$ to obtain the gravitational vacuum field equation in a
four-dimensional Finsler spacetime. To leading order in the post-Newtonian
approximation, we obtain the explicit form of the Finslerian line element. It
is simply the Schwarzschild's metric except for the Finslerian rescaling
coefficient $f(v)$ of the radial coordinate $r$, i.e. $R=f(v(r))r$. By setting
$f(v(r))=(1-\sqrt{a_0r^2/GM})^{-1}$, we obtain the famous MOND in a Finslerian
framework. Taking a dipole and a quadrupole term into consideration, we give
the convergence $\kappa$ in gravitational lensing astrophysics in our model.
Numerical analysis shows that our prediction is to a certain extent in
agreement with the observations of Bullet Cluster 1E0657-558. With the
theoretical temperature $T$ taking the observed value 14.8 keV, the mass
density profile of the main cluster obtained in our model is the same order as
that given by the best-fit King $\beta$-model.
