EXACT-SOLUTIONS WITH CONFORMAL KILLING VECTOR-FIELDS

Exact, perfect fluid solutions of Einstein's field equations admitting a Lie algebra of conformal Killing vectors are studied. A theorem by Defrise-Carter can be exploited to simplify the analysis considerably. A specific class of perfect fluid models admitting three conformal Killing vectors (with a particular group structure) acting on two-dimensional timelike surfaces is investigated. A particular exact perfect fluid solution is obtained which is physically well behaved (in the sense that p = p(mu), the weak and dominant energy conditions are satisfied, and it is amenable to a simple two perfect fluids interpretation), but it does not have a big-bang-like singularity. Further properties of this model are discussed. In addition, some examples of exact solutions and their particular conformal structures are presented.