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.

arXiv comment15 pages, 8 figures

References in corpus (24)

• A Universal Density Profile from Hierarchical Clustering
• The Structure of Cold Dark Matter Halos
• A direct empirical proof of the existence of dark matter
• Relativistic gravitation theory for the MOND paradigm
• THINGS: The HI Nearby Galaxy Survey
• Gravity, Lorentz Violation, and the Standard Model
• High-Resolution Rotation Curves and Galaxy Mass Models from THINGS
• Weak lensing mass reconstruction of the interacting cluster 1E0657-558: Direct evidence for the existence of dark matter
• A Textbook Example of a Bow Shock in the Merging Galaxy Cluster 1E0657-56
• The Baryonic Tully-Fisher Relation of Galaxies with Extended Rotation Curves and the Stellar Mass of Rotating Galaxies
• Modifying gravity with the Aether: an alternative to Dark Matter
• Distances to Galaxies from the Correlation Between Luminosities and Linewidths. III. Cluster Template and Global Measurements of H0
• Quasi-linear formulation of MOND
• Riemann-Finsler geometry and Lorentz-violating kinematics
• New Constraints on Neutrino Velocities
• On the Proof of Dark Matter, the Law of Gravity and the Mass of Neutrinos
• Finsler geometric extension of Einstein gravity
• 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 QUMOND galactic N-body code I: Poisson solver and rotation curve fitting
• A novel MOND effect in isolated high-acceleration systems
• Gravitational deflection of light in Rindler-type potential as a possible resolution to the observations of Bullet Cluster 1E0657-558

Cited by in corpus (16)

• Exact solution of vacuum field equation in Finsler spacetime
• Finsler spacetime geometry in Physics
• Limit on graviton mass from galaxy cluster Abell 1689
• Berwald spacetimes and very special relativity
• A unified description for dipoles of the fine-structure constant and SnIa Hubble diagram in Finslerian universe
• Inflation and primordial power spectra at anisotropic spacetime inspired by Planck's constraints on isotropy of CMB
• Galaxies Rotation Curves in the Grumiller's Modified Gravity
• Modified Dark Matter: Relating Dark Energy, Dark Matter and Baryonic Matter
• Black Hole Solutions with Constant Ricci Scalar in a Model of Finsler Gravity
• Finslerian perturbation for the $\Lambda$CDM model
• Primordial power spectrum of tensor perturbations in Finsler spacetime
• Effects of spacetime anisotropy on the galaxy rotation curves
• Finslerian dipolar modulation of the CMB power spectra at scales $2<l<600$
• Spatial and temporal variations of the fine-structure constant in the Finslerian universe
• Modified Dark Matter in Galaxies and Galaxy Clusters
• Finslerian MOND versus the Strong Gravitational Lensing of the Early-type Galaxies