Physics
Scientific paper
Mar 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990gregr..22..241c&link_type=abstract
General Relativity and Gravitation, Volume 22, Issue 3, pp.241-251
Physics
19
Scientific paper
Fluid space-times which admit a conformal Killing vector (CKV) are studied. It is shown that even in a perfect fluid space-time a conformal motion will not, in general, map the fluid flow lines onto fluid flow lines; consequently, perfect fluid space-times and, in particular, the simplest perfect fluid space-times known to admit a CKV, namely the Friedmann-Robertson-Walker (FRW) space-times, are studied. A direct proof that there do not exist any special CKV in FRW space-times will be given, thereby motivating the study of the physically more relevant proper CKV. Indeed, one of the principal motivations of the present work is the study of the symmetry inheritance problem for proper CKV. Since the FRW metric can, in general, satisfy the Einstein field equations for a non-comoving imperfect fluid, the relationship between the FRW models (and in particular the standard comoving perfect fluid models) and the conditions under which conformal motions (and in addition homothetic motions) map fluid flow lines onto fluid flow lines are investigated. Finally, further properties of fluid space-times which admit a proper CKV, and in particular space-times in which the CKV is parallel to the fluid four-velocity, are discussed.
Coley Alan A.
Tupper Brian O. J.
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