The weak field approximation

  • Thread starter Thrice
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  • #1
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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 [Broken]
http://img68.imageshack.us/img68/4677/2te4.jpg [Broken]
http://img68.imageshack.us/img68/7853/3jg9.jpg [Broken]
http://img68.imageshack.us/img68/6273/4qw8.jpg [Broken]
http://img68.imageshack.us/img68/273/5hu6.jpg [Broken]

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?
 
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Answers and Replies

  • #2
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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?
 
  • #3
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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.
 
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  • #4
999
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Also, just about every GR book goes through this derivation. It's sort of traditional.
 

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