Finslerian MOND vs. observations of Bullet Cluster 1E0657-558

TL;DR

This paper develops a Finslerian extension of MOND to better explain gravitational lensing observations of the Bullet Cluster, achieving partial agreement with empirical data.

Contribution

It introduces a Finslerian MOND framework incorporating anisotropic effects and demonstrates its potential to explain Bullet Cluster observations better than traditional MOND.

Findings

Finslerian MOND reproduces key features of Bullet Cluster lensing data.

The model's mass density profile aligns with observational fits.

Numerical results show partial agreement with observed temperature and mass distribution.

Abstract

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.