Spherically symmetric spacetimes admitting inheriting conformal Killing vector fields

Abstract

Perfect fluid spherically symmetric spacetimes admitting a proper inheriting conformal Killing vector (CKV) are studied. It is found that, other than Friedmann-Robertson-Walker (FRW) spacetimes, the only known examples of proper CKV perfect fluid spherically symmetric spacetimes in which the CKV is inheriting are conformal FRW spacetimes, static Schwarzschild interior spacetimes or generalized Gutman-Be'spalko-Wesson spacetimes and all of these spacetimes are either conformally flat or have a CKV which is either parallel to or orthogonal to the fluid 4-velocity. A general theorem is proven in which the (restricted) form of the CKV (and conformal factor) is given should a perfect fluid spherically symmetric spacetime admit a proper inheriting CKV. Various results on the non-existence of perfect fluid spherically symmetric spacetimes admitting a proper inheriting CKV are then derived, thereby providing further validity of a general non-existence conjecture (at least in the perfect fluid case).