What is the significance of the weak field approximation in general relativity?

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Discussion Overview

The discussion centers on the significance of the weak field approximation in general relativity (GR), particularly its relationship to Newtonian gravity and the derivations involved in demonstrating this connection. Participants explore the mathematical aspects and implications of these derivations within the context of GR.

Discussion Character

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

Main Points Raised

  • One participant expresses confusion about the derivations in the context of the weak field approximation and questions the necessity of how GR reduces to Newtonian mechanics.
  • Another participant asserts that GR must reduce to Newtonian gravity in the low velocity, weak field limit for consistency, suggesting that the derivations are valuable for practice with Einstein's equations.
  • A similar viewpoint is reiterated, emphasizing that while the reduction is known, the derivations serve as good practice.
  • It is noted that many GR textbooks include these derivations as a traditional approach.

Areas of Agreement / Disagreement

Participants generally agree on the importance of the weak field approximation and its connection to Newtonian gravity, but there is some disagreement regarding the necessity and clarity of the derivations involved.

Contextual Notes

Some participants express uncertainty about specific mathematical constraints and the rationale behind certain steps in the derivations, indicating potential limitations in understanding or assumptions made in the texts referenced.

Thrice
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Looks like I really don't have a feel for it. So I was working on this the other day.

(arranged in order)
http://img218.imageshack.us/img218/9613/1gx9.jpg
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http://img68.imageshack.us/img68/273/5hu6.jpg

It's fairly straightforward, but I think I'm just not used to the style. For example in 17.19 they took only the spatial equations because the metric doesn't change with time. Well just going by the math, I don't see any constraints on n. I see the constraints on k,j,p though. Do they translate to n as well? Same thing happens at 17.25. I figured you can choose to consider any parts of your system for whatever reason.

Then at 17.36 when they just dropped that entire term, but chose not to do the same with the 17.35 term. It works, though. The solution at the end is correct.

So I got to thinking .. What role do these derivations really play? Does it really matter how you show that GR reduces to Newtonian mechanics? GR is correct whether you do or not, right? I even saw a place where the author started with the metric for the Newtonian limit and 'derived' f=ma. It just seems like so much handwaving smoke and mirrors.

Of course I'm still new to all this so it's possible I didn't pay attention a few pages back. Thoughts?
 
Last edited by a moderator:
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GR has to reduce to Newtonian gravity in the low velocity, weak field limit to be a consistent theory. The derivations are also good practice in working with Einstein's equation, the connection, and the metric. What book is this from?
 
Daverz said:
GR has to reduce to Newtonian gravity in the low velocity, weak field limit to be a consistent theory. The derivations are also good practice in working with Einstein's equation, the connection, and the metric. What book is this from?
https://www.amazon.com/gp/product/012200681X/?tag=pfamazon01-20

If it's correct (and i figure there are other ways to verify that it's correct) then we already know that it reduces. But yeah it is good practice.
 
Last edited by a moderator:
Also, just about every GR book goes through this derivation. It's sort of traditional.
 

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