No abstract

We determine conformal symmetry classes for the pp-wave spacetimes. This refines the isometry classification scheme given by Sippel and Goenner (1986 Gen. Rel. Grav. 18 1229). It is shown that every conformal Killing vector for the null fluid type N pp-wave spacetimes is a conformal Ricci collineation. The maximum number of proper non-special conformal Killing vectors in a type N pp-wave spacetime is shown to be three, and we determine the form of a particular set of type N pp-wave spacetimes admitting such conformal Killing vectors. We determine the conformal symmetries of each type N isometry class of Sippel and Goenner and present new isometry classes.

A proper conformal Killing vector (CKV) in a fluid spacetime will be defined to be inheriting if fluid flow lines are mapped conformally by the CKV. 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 CKV. Generalizations of this result to non-comoving perfect fluid and comoving but non-perfect fluid synchronous spacetimes are then considered. Proper CKV spacetimes, and especially inheriting CKV 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).

Viscous heat-conducting fluid and anisotropic fluid space-times admitting a special conformal Killing vector (SCKV) are studied and some general theorems concerning the inheritance of the symmetry associated with the SCKV are proved. In particular, for viscous fluid spacetimes it is shown that (i) if the SCKV maps fluid flow lines into fluid flow lines, then all physical components of the energy-momentum tensor inherit the SCKV symmetry; or (ii) if the Lie derivative along a SCKV of the shear viscosity term 1]U ab is zero then, again, we have symmetry inheritance. All space-times admitting a SCKV and satisfying the dominant energy condition are found. Apart from the vacuum pp-wave solutions, which are the only vacuum solutions that can admit a SCKV, the energy-momentum tensor associated with these spacetimes is shown to admit at least one null eigenvector and can represent either a viscous fluid with heat conduction or an anisotropic fluid. No perfect fluid space-times can admit a SCKV. These SCKV space-times and, also, space-times admitting a homothetic vector are used to illustrate the symmetry inheritance theorems.2616