SPACETIMES ADMITTING INHERITING CONFORMAL KILLING VECTOR-FIELDS

A proper conformal Killing vector (C K V) in a fluid spacetime will be defined to be inheriting if fluid flow lines are mapped conformally by the C K V. The consequences of this definition are considered. In particular, a general class of spacetimes called synchronous spacetimes are investigated and it is proved that orthogonal synchronous perfect fluid spacetimes, other than Friedmann-Robertson-Walker spacetimes, admit no proper inheriting C K V. Generalizations of this result to non-comoving perfect fluid and comoving but non-perfect fluid synchronous spacetimes are then considered. Proper C K V spacetimes, and especially inheriting C K V spacetimes, are very rare, and a determination of all such spacetimes is of interest. In particular, it is conjectured that a non-existence result of the above form may be valid when generalized to spacetimes other than synchronous spacetimes (at least in the perfect fluid case). © 1990 IOP Publishing Ltd.