Why is the sign in Einstein's equation's RHS often presented differently?

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Discussion Overview

The discussion revolves around the presentation of the Einstein field equations (EFE) and the differing sign conventions used in the source term. Participants explore the reasons behind these variations and the implications of different contraction methods in tensor calculus.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions whether the absence of a minus sign in the source term of the EFE is due to a specific reason or simply carelessness.
  • Another participant references a Wikipedia article that discusses sign conventions related to the EFE.
  • A different participant explains that there are two methods of contraction when deriving the Ricci tensor from the Riemann curvature tensor, noting that the choice of contraction affects the sign due to the antisymmetry of the Riemann tensor.
  • One participant expresses confusion over the various conventions and points to a blog post for a more detailed explanation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the reasons for the differing sign conventions, and multiple viewpoints regarding the interpretation of these conventions remain present.

Contextual Notes

The discussion highlights potential limitations in understanding due to the dependence on specific definitions and the unresolved nature of the sign convention issue.

TrickyDicky
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Fast question :I noticed that often the EFE are presented without the minus sign in the source term, (G=kT instead of G=-kT) does that have some reason behind or is it just plain sloppiness?
 
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Hi, TrickyDicky.

There are two ways of contraction defined in getting Ricci tensor from Rieman curvature tensor, i.e. contraction of first two indexes and contraction of the first and last indexes. Since Rieman tensor is antisymmetric, two ways are different only in sign.

Regards.
 
Ok, thanks.
 
http://equatorfreq.wordpress.com/2010/08/13/signs-in-einsteins-equation/" is a more detailed explanation. I really find all these different conventions confusing.
 
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