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Riemann Curvature Tensor

  1. Apr 17, 2009 #1
    http://www.mth.uct.ac.za/omei/gr/chap6/frame6.html" is a derivation of the components of the riemann curvature tensor. the problem is that i can't understand the transition between eq97 and eq89 .
    what does "To lowest order " mean ???
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Apr 17, 2009 #2
    I'm not familiar at all with the notation (GR tends to have the most horrible formulas I've ever seen), but the first step looks like a use of the Fundamental Theorem of Calculus, and the approximation looks like some sort of truncated Taylor expansion.
     
  4. Aug 17, 2009 #3
    Hi, just found your question today. I am working through Dunsby's webpages which are almost identical to Schutz's" Introduction to General relativity". Ok , my understanding of eqns 92 to 97 are...
    He finds the change in the component V alpha when parallel transported around the loop to get eqn 97. The each pair of terms has the form... integral @ x=a + delta a MINUS integral @ x= a. This is just like delta f = df/ dx . delta x to first order .
    i take it there is some mathematical theorem that allows you to change d/dx of an integral into an integral of d/dx ... giving eqn 98.
    then using eqn 99 or 92 again we arrive at the Riemann curvature tensor

    PS. Does anyone else find that web pages and lecture notes on GR are poorly explained and very difficult to work through unaided??? I've self- studied Maths to degree level using OU courses and always found the reasoning well explained. BUT not GR!!!
    Cheers!
     
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