SYMMETRY INHERITANCE OF CONFORMAL KILLING VECTORS

Kinematics and dynamics in general relativity are clearly defined by considering the kinematical and dynamical variables and the identities and constraints they have to satisfy. Symmetries (collineations) are one important form of constraint that can be classified into various levels from Killing vectors to curvature collineations. A method is presented for writing the field equations for a general spacelike collineation xi(a) orthogonal to the four-velocity u(a) of the matter fluid and arbitrary matter. Applications are considered for spacelike conformal Killing vectors and matter described either by a perfect fluid or by an anisotropic fluid. The concept of symmetry inheritance is generalized to the case of a conformal Killing vector (CKV). It is shown that the symmetry of a proper spacelike CKV orthogonal to the four-velocity u(a) is not inherited by any type of matter.