Modified Newton's gravity in Finsler Space as a possible alternative to dark matter hypothesis

TL;DR

This paper derives a modified Newtonian gravity within Finsler geometry, which naturally explains galaxy rotation curves without dark matter, offering an alternative theoretical framework to MOND.

Contribution

It introduces a Finsler geometric approach to modify Newtonian gravity, aligning with MOND and explaining galactic rotation curves without dark matter.

Findings

Finsler structure yields MOND-like gravity

Galaxy rotation curves explained without dark matter

Provides a geometric foundation for modified gravity

Abstract

A modified Newton's gravity is obtained as the weak field approximation of the Einstein's equation in Finsler space. It is found that a specified Finsler structure makes the modified Newton's gravity equivalent to the modified Newtonian dynamics (MOND). In the framework of Finsler geometry, the flat rotation curves of spiral galaxies can be deduced naturally without invoking dark matter.