On the geometry of Petrov type II spacetimes

In general, geometries of Petrov type II do not admit symmetries in terms Killing vectors or spinors. We introduce a weaker form equations which solutions. particular, there is an analog the Penrose-Walker spinor. Some its properties, including associated conservation laws, are discussed. Perturbations Einstein complex scalar Debye potential yield solutions to linearized equations. The Weyl tensor shown be half N. remaining curvature component on algebraically special side reduced first order differential operator acting potential.