The Kerr-Schild pencil of metrics gab+Λl alb is investigated in the generic case when it maps an arbitrary vacuum space-time with metric gab 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 Kóta-Perjés metrics is a solution in the shearing class.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics