Plane symmetric spacetimes admitting inheriting conformal Killing vector fields

Abstract

Perfect fluid, plane symmetric spacetimes admitting a (proper) inheriting conformal Killing vector (ICKV) are studied. A result is proven on the general form that an ICKV can take in such a spacetime, which is then utilized to find all perfect fluid, plane symmetric ICKV spacetimes (subject to certain physical conditions). These spacetimes are discussed. In particular, we prove that if a perfect fluid, plane symmetric spacetime, in which the perfect fluid satisfies the barotropic equation of state and in which mu )0 and mu +p not=0, admits a (proper) ICKV, then the spacetime is necessarily at Friedmann-Robertson-Walker spacetime, or, possibly, a plane symmetric analogue of a generalized Gutman-Be'spalko-Wesson spacetime or a special static, shear-free spacetime.