LORENTZIAN 3-METRICS WITH DEGENERATE RICCI TENSORS

A classification of Lorentzian three-metrics whose Ricci tensor satisfies Rij = λ1gij + λ2v ivj with λ1 and λ 2(≠0) constant where vivi=κ(=0 or ±1) is given. An explicit coordinate representation is given for all the metrics that admit a G4 group as their maximal isometry group. Those metrics that admit a G3 as their maximal isometry group belong to either Bianchi class VI0, or VII0, or VIII, or IX when κ ≠ 0, and to either Bianchi class III, or IV, or VI0, VIh, or VIII when κ=0. An explicit coordinate representation is given for all the inhomogeneous solutions in the case κ≠0. © 1995 American Institute of Physics.