Generalized relativistic field equations have been derived for dynamics in a non-inertial reference frame interpreted as a Finsler space where events are specified by both spacetime coordinates and corresponding velocities (tangent vectors). The field equations follow in two alternative forms from exact general conservation laws derived through application of Cartan covariant differentiation within the framework of Finsler geometry. Velocity-dependent (curvature) terms in the field equations can account for the anisotropy of the gravitational field, together with the associated acceleration and expansion of the universe.

Generalized relativistic dynamics in a non-inertial reference frame

The possibility of a new extension of the general relativistc theory will be considered using Finsler geometry. The extension of Einstein’s general relativity can be expected to regard gravitational, electroweak, and strong interactive fields as geometrical structure of a spacetime based on Finsler geometry. Indeed, it will be shown that this theory can include the general theory of relativity under a certain special condition. In addition, Maxwell’s equations will be expressed using new metric representations of the electromagnetic vector and its tensor. Moreover, it will be suggested that this theory may include metric representations of weak and strong interactive fields.

Masatoshi Yazaki

Papers

A New extension of general relativistic theory