Скачать или смотреть General Relativity - General Tensors : Ricci Tensor and Einstein Tensor

The Ricci tensor and the Einstein tensor are the tensors of great importance in differential geometry and general relativity. To know the mysteries of curved spacetime the use of these two tensors is indispensable. Both of these are obtained by the process of contraction of a tensor. The Ricci tensor is obtained via contraction of Riemann Curvature tensor. It is found that it is a symmetric tensor of rank two having ten components. The Einstein tensor is obtained by applying the process of contraction on Bianchi identity. All the three forms- Covariant,Contravariant and Mixed of Einstein tensor have been defined. Divergence of Einstein’s tensor is zero,this fact is of immense significance in general relativity. When Ricci tensor is further contracted, the resulted object is the Curvature Scalar R.