Kretschmann scalar

Summary

The Kretschmann scalar is the full contraction $R_{abcd} R^{abcd}$ of the Riemann curvature tensor with itself. It is a scalar invariant, so it does not depend on the choice of coordinates. In general relativity it is used to tell real curvature singularities apart from coordinate artefacts. For the Schwarzschild metric it equals $48 G^2 M^2 / (c^4 r^6)$, which is finite at the horizon and infinite at $r = 0$.