Killing vectors in conformally flat perfect fluids via invariant classification
W Seixas · Classical and Quantum Gravity · 1992
The conditions for conformally flat perfect fluid spacetimes without expansion to admit Killing vectors were recently considered. This work shows the possibility of achieving the same results by a different approach. Considering the invariant classification of gravitational fields, basically the Karlhede classification, the conditions on the metric are determined by imposing functional dependence among the invariants. The continuous symmetries and consequently the number of Killing vectors are obtained naturally from the theory.