After finding the Einstein Tensor

  • Thread starter Reedeegi
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  • #1
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Main Question or Discussion Point

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?
 

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  • #2
atyy
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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.
 
  • #3
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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.
 
  • #4
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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
 

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