Field equations fully written out

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Discussion Overview

The discussion revolves around the request for a fully expanded form of the Einstein field equations, specifically expressed in terms of the coefficients of the metric tensor and their derivatives. The inquiry touches on the theoretical and conceptual aspects of general relativity and the utility of tensor notation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant requests a link to the fully written out Einstein field equations, expressing curiosity about their complexity.
  • Another participant suggests that the original poster (OP) should attempt to write them out themselves, emphasizing the educational value of the exercise.
  • A different participant questions the necessity of such an endeavor, arguing that the use of tensor notation is intended to avoid the complexity of fully expanding the equations.
  • One participant recommends using a computer algebra system, specifically mentioning the maxima or wxmaxima program with the ctensor package, to generate the equations, while predicting that the OP may find the task tedious.

Areas of Agreement / Disagreement

Participants express differing views on the value of fully expanding the Einstein field equations. While some encourage the OP to pursue the task, others argue against its practicality and educational merit. No consensus is reached regarding the necessity or usefulness of the exercise.

Contextual Notes

Participants note that the task of fully expanding the equations may be cumbersome and time-consuming, suggesting that it may not yield significant educational benefits. There is also an implication that the complexity of the equations is a reason for using tensor notation.

greypilgrim
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Hi,

Does anybody know a link where the Einstein field equations are fully written out, i.e. in terms of only the coefficients of the metric tensor and derivatives on the left side? I'm just curious how huge this must be.
 
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Write them yourself. No spoon feeding on PF.
 
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greypilgrim said:
Does anybody know a link where the Einstein field equations are fully written out, i.e. in terms of only the coefficients of the metric tensor and derivatives on the left side? I'm just curious how huge this must be.

I don't know why anyone would want to do such a thing - avoiding such overkill is precisely one of the reasons why we use tensor notation. But if you are really curious, you can always try and do this yourself - start with the expression for the Einstein tensor in terms of the metric and the Christoffel symbols, and simply expand all terms and sums. HINT : you are going to need a lot of patience, and a lot of paper :nb)
 
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dextercioby said:
Write them yourself. No spoon feeding on PF.
Markus Hanke said:
I don't know why anyone would want to do such a thing - avoiding such overkill is precisely one of the reasons why we use tensor notation. But if you are really curious, you can always try and do this yourself - start with the expression for the Einstein tensor in terms of the metric and the Christoffel symbols, and simply expand all terms and sums. HINT : you are going to need a lot of patience, and a lot of paper :nb)

I don't think this is an issue of spoon feeding as the educational value of what the OP is asking for is pretty minimal at best (maybe as a wallpaper design?). I think we all know (hope?) that the OP will give up before achieving the objective.

So, to the OP:
I would advise you to obtain the maxima or wxmaxima program with the ctensor package, set up a metric with all components present and use the ctensor features to generate the output of Einstein's Equation. I can pretty much guarantee that you will get bored and abandon the attempt before the answer has even finished scrolling by. But at least you will have learned something nontrivial about using a computer algebra system, which you might well find useful at some point in the future.
 
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