Harmonic coordinate
= Harmonic coordinate
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A harmonic coordinate satisfies $\Delta_gx^\lambda=0$ for a <Riemannian metric>, or $\Box_gx^\lambda=0$ for a <Lorentzian metric>. Equivalently $g^{\mu\nu}\Gamma^\lambda_{\mu\nu}=0$ or $\partial_\mu(\sqrt{|\det g|}\,g^{\lambda\mu})=0$. This common coordinate condition applies in both <Riemannian geometry> and <general relativity>.