# Switching from an accelerated frame of reference to a locally inertial reference system

Using the equivalence principle, show that the interval for an accelerated observer ($\textbf{g}$ uniform and constant) has the form $$ds^2|_{\text{first order in }\textbf{g}}=(1+2\varphi/c^2)c^2dt^2-d\textbf{x}^2+o(1/c^2),$$ where $\varphi=-\textbf{x}\cdot\textbf{g}$.

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What have you tried? Where are you stuck? –  Jerry Schirmer Apr 7 '13 at 17:00
also, what is $\phi$? –  Jerry Schirmer Apr 7 '13 at 17:00
@JerrySchirmer, physics.stackexchange.com/questions/59589/…;, and $\varphi=-\textbf{x}\cdot\textbf{g}$ –  ivax Apr 7 '13 at 17:06