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

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 $f(v(r))=(1-\sqrt{a_0{r}^2/GM}{)}^{-1}$, 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.

15 pages, 8 figures

References in corpus (9)

• A direct empirical proof of the existence of dark matter
• High-Resolution Rotation Curves and Galaxy Mass Models from THINGS
• Riemann-Finsler geometry and Lorentz-violating kinematics
• On the Proof of Dark Matter, the Law of Gravity and the Mass of Neutrinos
• The Bullet Cluster 1E0657-558 evidence shows Modified Gravity in the absence of Dark Matter
• Can MOND take a bullet? Analytical comparisons of three versions of MOND beyond spherical symmetry
• Modified Newton's gravity in Finsler Space as a possible alternative to dark matter hypothesis
• Catching a bullet: direct evidence for the existence of dark matter
• A novel MOND effect in isolated high-acceleration systems

Cited by in corpus (5)

• A unified description for dipoles of the fine-structure constant and SnIa Hubble diagram in Finslerian universe
• Galaxies Rotation Curves in the Grumiller's Modified Gravity
• Black Hole Solutions with Constant Ricci Scalar in a Model of Finsler Gravity
• Finslerian dipolar modulation of the CMB power spectra at scales $2<l<600$
• Modified Dark Matter in Galaxies and Galaxy Clusters