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D'Inverno Problem 19.5

  1. Jan 9, 2012 #1

    TerryW

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    Has anyone worked all the way through D'Inverno Chapter 19 Problem 19.5?

    I've had a good thrash at it - it is quite a bit of work, but I haven't been able to get to a satisfactory conclusion. I've worked out all the components of gab and Jab (for the cartesian frame) but when when I work through the transformations into the spherical co-ordinates, I get the correct answers for g'00, g'02, g'03, g'12, g'22, g'23 and g'33. The results for g'10, g'11, g'13 just will not come out with results that let me work through to the end of the problem successfully. The result for g'12 is fine and for this I used all the components of g'ab and Jab (except for g00) which is trivial.

    In the case of g'10, my result has a divisor of (r2+a2), but I've worked through two different ways to find that the answer probably ought to have a divisor of Δ. I just cannot see where this can come from given the values for gab and Jab.

    Any ideas anyone?


    Regards

    TerryW
     
  2. jcsd
  3. Jan 9, 2012 #2
    Would you mind posting the problem?
     
  4. Jan 10, 2012 #3

    TerryW

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    Hi Elfmotat,

    I've a pdf with the relevant information from pages 251 and 252 of D'Inverno. The problem is as follows:

    Apply the transformation (19.29) to (19.28) and then the transformation (19.24) to the result, to obtain the form (19.27).

    Clearly the answer to part 1 is going to be something like (19.22). I used this idea to 'reverse engineer' g'01 leaving me with two expressions which were the same apart from a term which is r2 + a2 when I do the transformation and Δ (as defined by(19.26) when I do the 'reverse engineer'.

    I'm going to see what happens if I replace r2 + a2 with Δ in (19.28), Maybe you can spot what is going wrong.

    Regards


    TerryW
     

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