Integration in the GHP formalism. IV: A new Lie derivative operator leading to an efficient treatment of Killing vectors (Q1585711)

Investigated are relationships between isometries and tetrads in general relativity theory. The authors concentrate on the Geroch-Held-Penrose integration procedure [\textit{R. Geroch, A. Held} and \textit{R. Penrose}, J. Math. Phys. 14, 874-881 (1973; Zbl 0875.53014)] using intrinsic GHP tetrads. From the results: A solution with four intrinsic GHP coordinates (intrinsic scalars of weight \(\{0,0\}\)) has no Killing vector. If there are only three intrinsic GHP coordinates, then a simple criterion allows to decide on the existence of a Killing vector. The situation becomes much more involved if only two intrinsic GHP coordinates exist. Seven explicit examples are discussed. -- For Part III, cf. ibid. 29, 1309-1328 (1997; Zbl 0893.53034).