The Kretschmann curvature scalar is defined to be K = RabcdRabcd where Rabcd is the Riemann tensor. I believe I heard in class that this scalar can be used to demonstrate the existence of a curvature singularity. Can somebody tell me why this is so? Also, I heard that it is better (easier I suppose) to use this Kretschmann curvature scalar rather than examining the Riemann curvature tensor component by component, to achieve this conclusion. Can someone help explain why (and how maybe?) we can demonstrate the existence of the singularity in the first place? Thanks in advance.