## Abstract

An example from a perfect fluid FRW space-time is presented to show that a conformal Killing vector (CKV) need not map fluid flow lines into fluid flow lines. Kinematic properties of the Lie derivative along a CKV of timelike and spacelike unit vectors are derived and applied to the fluid unit four-velocity vector. Dynamic properties of special conformal Killing vectors (SCKV) in a fluid with anisotropic pressure and vanishing energy flux are obtained using Einstein's field equations. It is shown that a SCKV maps both fluid flow lines and integral curves of n^{a} into themselves, where n^{a} is the unit spacelike vector of anisotropy. The relation between the anisotropic pressure components and the energy density is considered. By means of an example from a radiationlike viscous fluid FR W space-time it is shown that the dynamic results depend crucially on the vanishing of the energy flux vector. The extension of the dynamic results to a fluid with arbitrary stress tensor and zero energy flux vector is examined.

Original language | English |
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Pages (from-to) | 2987-2994 |

Number of pages | 8 |

Journal | Journal of Mathematical Physics |

Volume | 27 |

Issue number | 12 |

DOIs | |

Publication status | Published - 1 Jan 1986 |