Solve General Relativity Equation: Steps & Tips

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Discussion Overview

The discussion revolves around the steps involved in solving equations related to general relativity, specifically focusing on the transition between two equations and the implications of a weak field approximation. The scope includes mathematical reasoning and conceptual clarification.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant expresses confusion about the transition between two equations and seeks clarification.
  • Another participant identifies the context as a weak field approximation and questions the meaning of "weak field" in this context.
  • A suggestion is made to use the binomial expansion to facilitate the transition between equations, with a specific approximation provided for first order in ##1/c^2##.
  • A later reply acknowledges the suggestion and expresses a willingness to explore the binomial expansion further.
  • Another participant raises a concern about the lack of familiarity with the binomial expansion, implying potential gaps in mathematical knowledge relevant to general relativity.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the understanding of the weak field approximation or the mathematical tools required, indicating that multiple views and levels of understanding remain in the discussion.

Contextual Notes

There are indications of missing mathematical knowledge that may affect the discussion, particularly regarding the binomial expansion and its application in general relativity.

The black vegetable
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Maybe I'm just being stupid, missing something simple ? How do you get from the top two equations to the second equation? Many thanks
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It's a weak field approximation. What could "weak field" mean here?
 
You could use the binomial expansion.

##(1+ \frac{\phi_a}{c^2})^{-1} \approx (1 - \frac{\phi_a}{c^2})##

The quoted result is to first order in ##1/c^2##.
 
ah that's great thank you, I will look into binomial expansion, never met it before :)
 
You're doing general relativity, but have never seen the binomial expansion before? Be cautious about other mathematical knowledge lacking then, I'd say. Good luck anyway ;)
 
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