Covariant Derivation of the Ricci Tensor: Einstein's Method Now Online

Click For Summary
SUMMARY

The complete derivation of the covariant derivative of the Ricci Tensor, following Einstein's original methodology, is now accessible online at the provided link. The discussion highlights a common mistake regarding the use of indices, specifically the incorrect application of two lower μ indices. Participants emphasize the importance of adhering to the upper/lower covariant derivative convention to avoid confusion in tensor calculations.

PREREQUISITES
  • Understanding of tensor calculus
  • Familiarity with general relativity concepts
  • Knowledge of covariant derivatives
  • Proficiency in manipulating indices in tensor equations
NEXT STEPS
  • Study the derivation of the Ricci Tensor in detail
  • Learn about the implications of covariant derivatives in general relativity
  • Review the conventions for raising and lowering indices in tensor notation
  • Explore additional resources on Einstein's original works in general relativity
USEFUL FOR

Students and researchers in theoretical physics, mathematicians specializing in differential geometry, and anyone interested in the intricacies of general relativity and tensor analysis.

nobraner
Messages
11
Reaction score
0
The full derivation of the covariant derivative of the Ricci Tensor as Einstein did it, is now available on line at

https://sites.google.com/site/generalrelativity101/appendix-c-the-covariant-derivative-of-the-ricci-tensor

For those who wish to study it.
 
Physics news on Phys.org


nobraner, Your expressions all have two lower μ indices, which is incorrect. Would you like to raise one of them by inserting a gμν?
 


Bill,

Finally found the time to fix this. One of my biggest weaknesses is ignoring the upper/lower covariant derivative convention. I guess I always think of covariant derivatives as always being covariant.
 

Similar threads

Undergrad Ricci Tensor: Covariant Derivative & Its Significance
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Landau-Lifshitz pseudotensor - expressing the EM tensor ##T^{ik}##
  • · Replies 6 ·
Replies
6
Views
1K
Graduate Covariant Derivative Wrt Superscript Sign: Explained
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Relation between affine connection and covariant derivative
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Calculating Covariant Derivative of Riemann Tensor in Riemann Normal Coordinates
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Double contraction of curvature tensor -> Ricci scalar times metric
  • · Replies 2 ·
Replies
2
Views
3K
Graduate The derivation of the volume form in Ricci tensor
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Weyl tensor and coordinate acceleration
  • · Replies 12 ·
Replies
12
Views
2K
Graduate Understanding the Ricci Curvature Tensor in Einstein's Field Equations
  • · Replies 7 ·
Replies
7
Views
4K
Graduate Draft re Ricci vs Riemann tensors
  • · Replies 1 ·
Replies
1
Views
2K