Mathematical properties of a class of four-dimensional neutral signature metrics

摘要

While the Lorentzian and Riemannian metrics for which all polynomial scalar curvature invariants vanish (the VSI property) are well-studied, less is known about the fourdimensional neutral signature metrics with the VSI property. Recently it was shown that the neutral signature metrics belong to two distinct subclasses: the Walker and Kundt metrics. In this paper we have chosen an example from each of the two subcases of the Ricci-flat VSI Walker metrics respectively.