Special conformal Killing vector space-times and symmetry inheritance

Abstract

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 space-times 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 ησab 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 space-times 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.