GRADIENT CONFORMAL KILLING VECTORS AND EXACT-SOLUTIONS

We establish a connection between conformally related Einstein spaces and conformal killing vectors (CKV). We begin with the conformal map and prove that (a) under the conformal mapping (g) over bar(ik) = w(-2)g(ik), the necessary and sufficient condition for the tracefree part of the Ricci tenser (S-ik = R(ik) - (R/4)g(ik)) to remain invariant is that w,(i) is a CKV of g(ik) and (b) the most general form for w for conformally flat Einstein space, which is the de Sitter space, is composed of three terms each of which alone represents a hat space. The existence of gradient CKV (GCKV) is examined in relation to vacuum and perfect fluid spacetimes.