Kerr-Schild metrics revisited I. The ground state

The Kerr-Schild pencil of metrics $g_{ab}+\text{La}{l}_a{l}_b$ is investigated in the generic case when it maps an arbitrary vacuum space-time with metric $g_{ab}$ to a vacuum space-time. The theorem is proved that this generic case, with the field $l$ shearing, does not contain the shear-free subclass as a smooth limit. It is shown that one of the K'ota-Perj'es metrics is a solution in the shearing class.