Geodesic Deviation: Deriving Formula with Schtuz's Book

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SUMMARY

The discussion centers on deriving the formula for geodesic deviation using Schutz's book as a primary resource. Participants note that this approach is more straightforward than that presented in Misner, Thorne, and Wheeler's (MTW) text, despite its reliance on a specific coordinate system. The conversation highlights the importance of using an inertial coordinate system to clarify the physics involved. Additionally, a derivation based on Ohanian's work is referenced, indicating a collaborative effort to simplify complex concepts.

PREREQUISITES
  • Understanding of general relativity concepts
  • Familiarity with Schutz's "A First Course in General Relativity"
  • Basic knowledge of differential geometry
  • Experience with inertial coordinate systems
NEXT STEPS
  • Study the derivation of geodesic deviation in Schutz's book
  • Explore Misner, Thorne, and Wheeler's treatment of geodesic deviation
  • Review Ohanian's explanations on geodesic deviation
  • Investigate the implications of using different coordinate systems in general relativity
USEFUL FOR

Students and researchers in physics, particularly those focusing on general relativity and geodesic motion, will benefit from this discussion.

Terilien
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Can someone explain how to derive the formula for geodesic deviation? i didn't quite understand it. I'm using schtuz's book.
 
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You can try, for instance, http://www.mth.uct.ac.za/omei/gr/chap6/node11.html

This seems like a rather direct and straightforwards approach to me, even more direct than MTW's. Of course it is a bit mathematically impure, in that it assumes a convenient coordinate system, but I think assuming an inertial coordinate system for one of the observers makes the physics more apparent.
 
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Terilien said:
Can someone explain how to derive the formula for geodesic deviation? i didn't quite understand it. I'm using schtuz's book.
The derivation I placed on my web page at

http://www.geocities.com/physics_world/gr/geodesic_deviation.htm

started out being a translation from Ohanian's book to my web page. However it seemed to end up being Ohanian's book and part of what I had to say since Ohanian made somethings hard to understand there. Enjoy. Any problems then e-mail me so we can set straight if there is something wrong.

Pete
 

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