Curvature sign convention (source code)

= Curvature sign convention
{title2=$R_{\rm reversed}=-R$}

Definitions of the <Riemann curvature tensor> can differ by an overall sign, independent of the <metric signature>. Reversing that definition reverses the <Ricci tensor>, <Ricci scalar> and <Einstein tensor>, as well as the <curvature> side of the <geodesic deviation> identity and the <Palatini identity>. A derivation must choose the contraction and <derivative> ordering explicitly before combining formulas from different conventions. Changing a <metric signature> alone is a separate operation.