LANCZOS SPINTENSOR FOR THE ROBINSON-TRAUTMAN METRICS OF THE VACUUM SPACE AND EINSTEIN-MAXWELL FIELDS

Using the Newman-Penrose formalism, we obtain the Omega(r) projections of the Lanczos spintensor over the null tetrad for the Robinson-Traut man (RT) solutions of the vacuum space and Einstein-Maxwell fields. Sp ecifically, we are concerned with the Weyl-Lanczos relationships for t he II, III and D Petrov's type of the RT afore-mentioned metrics. The presented approach considers the most general case of the functions P( x(1), x(2), u) and H(x(1), x(2), r, u), that characterize the metrics, resulting in a procedure by far simpler than equivalent methods that use spinors and tensors in order to determine the K-ijr Lanczos spinte nsor.