Static vacuum conformal spatial metric
= Static vacuum conformal spatial metric
{title2=$ds^2=-e^{2U}dt^2+e^{-2U}\gamma_{ij}dx^idx^j$}
Rescaling the spatial metric by the squared static <lapse function> gives a useful three-dimensional quotient metric $\gamma$. In <Vacuum Einstein equations>, its <Ricci tensor> obeys $R_{ij}(\gamma)=2\partial_iU\,\partial_jU$, while $U$ is <harmonic>. The <contracted Bianchi identity> recovers the harmonic equation without dividing at critical points.