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I'm trying the exercises on p35 of the following:

http://arxiv.org/PS_cache/gr-qc/pdf/9707/9707012v1.pdf

I have done parts (i) and (ii) but was wondering if anybody can help me with (iii)?

I had [itex]k \cdot D k^\mu |_{U'=0} = k^\nu D_\nu k^\mu |_{U'=0} = k^V' D_{V'} k^\mu[/itex] since setting [itex]U'=0[/itex] means only the [itex]\nu=V'[/itex] componeent will contribute.

Subbing in we end up with

[itex]\kappa V' ( k^\mu{}_{, V'} + \Gamma^\mu{}_{V' \rho} k^\rho)[/itex]

I can't really make anything useful out of this now though?

Thanks.

http://arxiv.org/PS_cache/gr-qc/pdf/9707/9707012v1.pdf

I have done parts (i) and (ii) but was wondering if anybody can help me with (iii)?

I had [itex]k \cdot D k^\mu |_{U'=0} = k^\nu D_\nu k^\mu |_{U'=0} = k^V' D_{V'} k^\mu[/itex] since setting [itex]U'=0[/itex] means only the [itex]\nu=V'[/itex] componeent will contribute.

Subbing in we end up with

[itex]\kappa V' ( k^\mu{}_{, V'} + \Gamma^\mu{}_{V' \rho} k^\rho)[/itex]

I can't really make anything useful out of this now though?

Thanks.

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