Extrinsic curvature with a negative shift
= Extrinsic curvature with a negative shift
{title2=$K_{ij}=-(\dot h_{ij}+D_iN_j+D_jN_i)/(2N)$}
For $ds^2=-N^2dt^2+h_{ij}(dx^i-N^idt)(dx^j-N^jdt)$ and the future unit normal, the convention $K_{ij}=-n_{i;j}$ gives $K_{ij}=-(\dot h_{ij}+D_iN_j+D_jN_i)/(2N)$. Lower the <shift vector> with $h$. The sign of the shift terms changes when the opposite threading convention is used.