Has anyone worked all the way through D'Inverno Chapter 19 Problem 19.5?(adsbygoogle = window.adsbygoogle || []).push({});

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 g_{ab}and J_{ab}(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 J_{ab}(except for g_{00}) which is trivial.

In the case of g'_{10}, my result has a divisor of (r^{2}+a^{2}), 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 g_{ab}and J_{ab}.

Any ideas anyone?

Regards

TerryW

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# D'Inverno Problem 19.5

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