Riemannian Curvature Tensor in the Cartesian Coordinate Using the Golden Metric Tensor

Abstract

The golden metric tensor completes Euclidean geometry. Since geometry is the foundation of theoretical physics, it implies that our discovery of the golden metric paves way for redefining almost everything in theoretical physics. In this paper, we show how to express the Riemannian curvature tensor in terms of the golden metric tensor for all gravitational fields in nature in the cartesian coordinate. These results which are mathematically most elegant, physically most natural and satisfactory are further used to derive the Riemannian curvature scalar and ricci curvature tensor in the cartesian coordinate.