All spacetimes with vanishing curvature invariants
  All Lorentzian spacetimes with vanishing invariants constructed from the Riemann tensor and its covariant derivatives are determined. A subclass of the Kundt spacetimes results and we display the corresponding metrics in local coordinates. Some potential applications of these spacetimes are discussed. 
V. Pravda, A. Pravdova, A. Coley, R. Milson