Riemannian Acceleration in Cartesian Coordinate Based Upon the Golden Metric Tensor

Abstract

Geometric quantities in all orthogonal curvilinear co-ordinates are built upon Euclidean geometry. This geometry is founded on a well known metric tensor called the Euclidean metric tensor. Riemannian geometry which is assumed to be more general than the Euclidean geometry was founded on an unknown metric tensor for spacetimes in gravitational fields. Therefore the Riemannian geometry itself could not be opened up for exploration and exploitation, let alone the possible application to theoretical physics. But with the discovery of a general Riemannian metric tensor called the golden metric tensor, exploitation of Riemannian geometry is now possible. We are in a position to calculate all the theoretical predictions of Riemann’s geometrical and physical concepts and principles and compare them with experimental physical evidence. In this paper, we use the golden metric tensor to develop Riemannian acceleration in the Cartesian coordinate for application in theoretical physics and other related fields.