Homothety groups in space-time (Q912401)

The authors investigate Lorentzian space-times which admit an r- dimensional Lie algebra of homothetic vector fields at least one of which is proper homothetic (i.e., it is not a Killing vector field). A complete description of the situation is obtained if \(r\geq 6\) and some results are given for \(r\leq 5\). Based on these results the authors also consider space-times which admit affine vector fields. They establish the maximal dimension of the Lie algebra of affine vector fields and construct examples when the dimension of this algebra is high.