# Static charge in an accelerated frame

In special relativity the metric of an accelerated frame is $$ds^2= (1-2 a_j x^j)dt^2 + 2 \Omega_{m j}x^j dx^m dt + \eta_{ml}dx^m dx^j$$ where the sums over latin indices go from 1 to 3. Let's suppose we have a static charge in the origin of our coordinate system. Is there an approximate solution of the Maxwell equations for that point charge?

• For clarification: Is the charge sitting at a fixed value of the spacelike coordinates in a non-accelerated-frame coordinate system or in the accelerated-frame coordinate system? The title suggests the former, but the wording in the body suggests the latter, unless I'm misinterpreting the wording "our coordinate system". – Chiral Anomaly May 14 at 12:21
• The charge is sitting at fixed spacelike coordinates in the accelerated frame. – yasalami May 14 at 13:42
• The metric that you wrote is generally non-flat. For $\Omega=0$ the Kottler-Møller metric would be recovered if $g_{tt}$ element is $-(1-a x)^\color{red}{2}$. – A.V.S. May 14 at 22:13