Einstein tensor fully written out

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    Einstein Tensor
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Discussion Overview

The discussion revolves around the request for a complete expression of the Einstein tensor, focusing on its formulation in terms of the metric and its derivatives. Participants explore the complexity involved in deriving this expression and the notation used in general relativity.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about resources for a fully written-out Einstein tensor, indicating an interest in understanding the underlying details of the notation.
  • Another participant suggests that the only way to obtain the full expression is to derive it independently, implying a significant effort is required.
  • A different participant provides a formula for the Riemann tensor in terms of Christoffel symbols, indicating a pathway to derive the Einstein tensor through contraction and differentiation.
  • A link to a Wikipedia page is shared, which may contain relevant information about the Einstein tensor.

Areas of Agreement / Disagreement

There is no clear consensus on the best approach to obtain the fully written-out Einstein tensor, with some participants advocating for independent derivation while others provide resources and formulas.

Contextual Notes

The discussion does not resolve the complexity of deriving the Einstein tensor, and participants express varying levels of familiarity with the mathematical tools involved.

greypilgrim
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Hi,

Does somebody know a link where the Einstein tensor is fully written out, i.e. only containing the metric and its derivatives? I'm just wondering how much is actually hidden in the notation.
 
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There;s only message anyone can give: write it out yourself.
 
Yes, it takes ages. This is the Riemann tensor in terms of Christoffel symbols

##{R^{r}}_{msq}=\Gamma ^{r}_{mq,s}-\Gamma ^{r}_{ms,q}+\Gamma ^{r}_{ns}\Gamma ^{n}_{mq}-\Gamma ^{r}_{nq}\Gamma ^{n}_{ms}##

the ',' before an index is differentiation. Contract on idexes r and s and you have the Ricci tensor, etc.
 

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