HOMOGENEOUS SPACE-TIMES WITH 7 ISOMETRIES

A new homogeneous space-time with seven isometries is derived by means of a complex transformation. It is shown that it is conformally flat and its Weyl-flat form is exhibited. Its Killing vector fields and the corresponding Lie algebra are also presented. An integral representation of these vector fields is found. Sources for the new space-time geometry are obtained by combining Synge's approach to Einstein's equations with energy conditions and Segre classification of the energy-momentum tensors. A comparison with other rare space-times possessing a G7 of motions is made by using a suite of computer algebra programs.