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

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.