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## Homework Statement

Calculate the four velocity [itex] V^i [/itex], the four acceleration [itex] A^i [/itex] and the scalar [itex] A^i A_i [/itex] for an observer at [itex] r=r_0, \theta = \theta_0, \phi = \phi_0 [/itex] in the Schwarzschild spacetime with r>2m.

## Homework Equations

The Schwarzschild Metric

[tex] ds^2 = -\displaystyle \left(1-\frac{2m}{r} \right) dt^2 + \left( 1- \frac{2m}{r} \right)^{-1} dr^2 + r^2 \left( d\theta ^2 + sin^2(\theta) d\phi ^2 \right) [/tex]

## The Attempt at a Solution

I'm not too sure how to even start this problem in that I don't see how the four velocity will depend on the metric, and so the only place I can see it being needed is in calculating the scalar [itex] A^i A_i [/itex]. Is the spatial part of the four velocity given by the spherical velocity [itex] ( \dot{r}, r \dot{\theta}, r \dot{\theta} sin(\theta) ) [/itex] and the time element would just be 1? (we've scaled c= 1).