I've been working on a problem that I can't seem to get started on. Here is how it is posted:(adsbygoogle = window.adsbygoogle || []).push({});

Metric of a space is:

[itex] ds^2 = (1+2\phi^2)dt^2 - (1-2\phi)(dx^2+dy^2+dz^2)[/itex], where [itex] |\phi | << 1 [/itex] everywhere. Given a point [itex](t_0 , x_0 , y_0, z_0)[/itex] find a coordinate transformation to a locally inertial frame to first order in [itex]\phi[/itex]. At what rate does this frame accelerate with respect to the original coordinates (to first order in [itex]\phi[/itex])?

So far I know that I have to find a transformation that transforms the metric to the Minkowski metric, [itex]\eta_{ab}[/itex] so that [itex]ds^2 = \eta_{ab}dx'^a dx'^b [/itex] but I'm not sure how to get started on this.

I'm studying this myself so I have no instructor to ask so hopefully someone can point me along the right geodesic in this space of confusion. ;)

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# Transformation to local inertial frame

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