$\mathcal{I}$-degenerate pseudo-Riemannian metrics
  In this paper we study pseudo-Riemannian spaces with a degenerate curvature structure i.e. there exists a continuous family of metrics having identical polynomial curvature invariants. We approach this problem by utilising an idea coming from invariant theory. This involves the existence of a boost which is assumed to extend to a neighbourhood. This approach proves to be very fruitful: It produces a class of metrics containing all known examples of $\mathcal{I}$-degenerate metrics. To date, only Kundt and Walker metrics have been given, however, our study gives a plethora of examples showing that $\mathcal{I}$-degenerate metrics extend beyond the Kundt and Walker examples.   The approach also gives a useful criterion for a metric to be $\mathcal{I}$-degenerate. Specifically, we use this to study the subclass of VSI and CSI metrics (i.e., spaces where polynomial curvature invariants are all vanishing or constants, respectively). 
Sigbjorn Hervik, Anders Haarr and Kei Yamamoto
math-ph gr-qc math.MP