Einstein equations in a weakly gravitational complex Finsler space

Abstract

In this paper, we give a two-dimensional complex Finsler model for the real gravitation space-time. The study of the weakly gravitational field leads to some interesting geometrical and physical aspects, such as the study of curvature invariants with respect to the complex Berwald frames. A generalization of the Einstein equations is proposed for a two-dimensional complex Finsler space and these are written with respect to the directions of the complex Berwald frame attached. Some conditions are required so that the energy of the space should be conservative. In all these results the curvature invariants play a special meaning.