Jef. Skea, A spacetime whose invariant classification requires the fifth covariant derivative of the Riemann tensor, CLASS QUANT, 17(8), 2000, pp. L69-L74
We present the first example of a metric whose invariant classification req
uires the fifth covariant derivative of the Riemann tensor. The existence o
f this metric raises the known practical bound for invariant classification
s, reconciles the theoretical and practical upper limits for invariant clas
sifications of Petrov type N spacetimes, and brings the practical limits fo
r invariant classifications to within one of the theoretical limits for a s
pacetime in general.