Effects of spacetime anisotropy on the galaxy rotation curves

TL;DR

This paper investigates how spacetime anisotropy, modeled through Finsler geometry, affects galaxy rotation curves and finds that anisotropic effects become significant at low accelerations, aligning with MOND-like behavior.

Contribution

It introduces a Finslerian model to study spacetime anisotropy effects on galaxy rotation curves and relates the critical acceleration to cosmological parameters.

Findings

Anisotropic effects are significant when Newtonian acceleration is below a critical value.

The critical acceleration is of the order of 10^{-10} m/s^2, similar to MOND's acceleration scale.

The model links spacetime anisotropy with observed galaxy rotation phenomena.

Abstract

The observations on galaxy rotation curves show significant discrepancies from the Newtonian theory. This issue could be explained by the effect of the anisotropy of the spacetime. Conversely, the spacetime anisotropy could also be constrained by the galaxy rotation curves. Finsler geometry is a kind of intrinsically anisotropic geometry. In this paper, we study the effect of the spacetime anisotropy at the galactic scales in the Finsler spacetime. It is found that the Finslerian model has close relations with the Milgrom's MOND. By performing the best-fit procedure to the galaxy rotation curves, we find that the anisotropic effects of the spacetime become significant when the Newtonian acceleration \(GM/r^2\) is smaller than the critical acceleration \(a_0\). Interestingly, the critical acceleration \(a_0\), although varies between different galaxies, is in the order of magnitude \(cH_0/2\pi\sim 10^{-10} \rm{m\,\, s^{-2}}\).