Plane gravitational waves of gauge-invariant generalized field equations with asymmetric fundamental tensor in plane symmetry

Buchdahl [Q. J. Math. 8, 89 (1957) and 9, 257 (1958)] has proposed the study of gauge-invariant generalization of field theories with asymmetric fundamental tensor. In this paper, the solution of plane gravitational waves in these Buchdahl's field theories have been investigated by the authors in plane symmetric space-time. Plane symmetry was studied and defined by Taub [Ann. Math. 53, 472 (1951)]. It has been shown that these solutions become identical with those of strong field equations of Einstein’s nonsymmetric unified field theory in plane symmetry under certain cases.