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Could somebody please explain something regarding the Nordstrom metric?

In particular, I am referring to the last part of question 3 on this sheet -- about the freely falling massive bodies.

My thoughts: The gravitational effects would be significant since for a massive body, the geodesic is timelike. There woud thus be a $\eta^{\mu\delta}\partial_\delta \phi \dot x^\beta \dot x_\beta$ is not of the form $f(\lambda)\dot x^\mu$ so the affine parametrization does not eliminate this term containing the gravitational potential $\phi$.

Does this argument make any sense at all? Also, what more can I say about the geodesics of such massive particles?


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I did a quick Google and found loads of stuff about geodesics in Nordstrom gravity ... –  John Rennie Jan 22 '13 at 10:08
@JohnRennie: Yes, but I haven't been able to find anything directly addressing my problem. –  hetherson Jan 22 '13 at 10:45
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