After finding the Einstein Tensor

  • Context: Graduate 
  • Thread starter Thread starter Reedeegi
  • Start date Start date
  • Tags Tags
    Einstein Tensor
Click For Summary

Discussion Overview

The discussion centers on the properties and physical significance of the Einstein Tensor, particularly in the context of a specific metric. Participants explore its mathematical characteristics, such as its covariant derivative and relationship to the stress-energy tensor, while also questioning the physical implications of its determinant, trace, and matrix operations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant calculated the Einstein Tensor for a specific metric and inquired about its physical representation and the significance of its determinant, trace, and matrix operations.
  • Another participant noted that the covariant derivative of the Einstein tensor is zero, linking this to energy-momentum conservation in flat spacetime through the Einstein field equation.
  • A different participant explained that the Einstein tensor is a trace-reversed version of the Ricci tensor and emphasized its conservation property, stating that the divergence of the Einstein tensor vanishes.
  • It was mentioned that the Einstein tensor is physically identified with the stress-energy tensor, with references to literature for further explanation of the physical properties associated with it.

Areas of Agreement / Disagreement

Participants express various viewpoints on the significance and properties of the Einstein tensor, with no consensus reached on the specific physical meanings of its determinant, trace, or matrix operations.

Contextual Notes

The discussion does not resolve the implications of the determinant or trace of the Einstein tensor, nor does it clarify the assumptions underlying the physical interpretations presented.

Reedeegi
Messages
97
Reaction score
0
Before I begin, I stress that this is NOT a homework question but rather a self-study question.

In any case, I calculated the Einstein Tensor of a body with the metric diag[{2GM/r-1,0,0,0},{0,1+2GM/r,0,0},{0,0,1+2GM/r,0},{0,0,0,1+2GM/r}]. What does the Einstein Tensor represent? Does its determinant/trace/or matrix operations have any physical meaning?
 
Physics news on Phys.org
The covariant derivative of the Einstein tensor is zero, which by the Einstein field equation means the covariant derivative of the stress-energy-momentum tensor is zero, which is related to energy-momentum conservation in flat spacetime.
 
Basically, the Einstein tensor is a trace-reversed version of the Ricci tensor (a contraction of the Riemann curvature tensor). Its most salient feature is that it is conserved, in the following sense: [tex]G^{ab}_{;b} = 0[/tex]. In other words, the "divergence" of the Einstein tensor vanishes.
 
As was mentioned indirectly; the Einstein tensor is physically identified with the physical stress-energy tensor. The physical properties associated with the Stress-Energy tensor are explained in various books. The wikipedia article seems adequate:
http://en.wikipedia.org/wiki/Stress-energy_tensor

Ray
 

Similar threads

  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 6 ·
Replies
6
Views
1K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 27 ·
Replies
27
Views
3K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 10 ·
Replies
10
Views
4K
  • · Replies 16 ·
Replies
16
Views
3K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 3 ·
Replies
3
Views
1K