Writing the EFE in a different form

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Discussion Overview

The discussion revolves around the formulation of the Einstein Field Equations (EFE) expressed solely in terms of the metric tensor and the stress-energy tensor. Participants explore the complexity of this expression and seek resources or methods to derive it.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant inquires about resources for finding the EFE written in terms of the metric tensor and stress-energy tensor, noting the derivation of the Ricci Curvature tensor and Ricci scalar from the metric tensor.
  • Another participant suggests using software like Maxima, ctensor, or cadabra to generate the expression.
  • A different participant expresses unfamiliarity with the suggested software and asks if any websites might have the expression available.
  • One participant shares their past experience of reconstructing the expression for a presentation, mentioning the complexity and length of the resulting equation, which included many terms and lacked visible patterns.
  • A participant acknowledges the suggestion to reconstruct the expression by hand but indicates time constraints due to an impending school essay deadline.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the availability of the EFE in the desired form or the best method to derive it, indicating multiple competing views and unresolved questions regarding resources and complexity.

Contextual Notes

Limitations include the potential complexity of the expression and the participants' varying familiarity with software tools for generating the EFE.

Matterwave
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Anyone know where I can, possiblely, find the EFE's written only in terms of the metric tensor and the stress-energy tensor? I know that the Ricci Curvature tensor and the Ricci scalar are derived (eventually) from the metric tensor (after a roundabout way through Christoffel symbols). The expression, I would think would be immensely long, but is there a place that has it?
 
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You could probably generate it using software like Maxima and ctensor, or cadabra.
 
I.C. I'm not familiar with such software...do you think any website may have it?

It's not that important, I'd just like to see the thing so it becomes a little more concrete in my mind.
 
I did that for a presentation a couple of years ago, but I can't seem to find the latex file with the complete expression. As I remember, there were around 50 terms on the LHS, with all sorts of permutations of up to 4 factors of g per term, the whole thing looked remarkably messy and lacked any visible patterns.

You can reconstruct it by hand in less than an hour, starting here

http://en.wikipedia.org/wiki/Einstein_tensor
 
Ok, I may do that sometime...I just don't have the time right now hehe, essay for school due tomorrow, and I haven't started yet! D=
 

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