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?
Thanks.
