Re-expression of the Einstein tensor using basis vectors

Sahin AR

Published on: 2023-12-04

Abstract

We try a simple and different way to express the Einstein tensor, which is the fundamental equation of general relativity. We write Einstein tensor, which measures the curvature of any space, and its metric tensor, in terms of basis vectors, which are more fundamental quantities. Thus, we show that the freedom of the space-time studied can be reduced from 16 degrees of freedom to four by basis vectors. We also found that the Einstein tensor obtained in terms of basis vectors for space-time has the same form as the stress-energy tensor of electrodynamics.