Finsler geometry in GTR in the presence of a velocity dependent gauge field

Abstract

Fields around their source determine a curved geometry. Velocity-dependent phenomena in these fields involve a curvature tensor, whose elements depend on the value and the direction of the velocity of the source of the interaction gauge field, as observed from the reference frame of the matter field. This double (space-time and velocity) dependency of the curvature requires the field to follow a Finsler geometry.