Plane waves in the general theory of relativity

The Newman-Penrose method is used to study the class of gravitational fields in a vacuum which permit a normal congruence of isotropic geodesies. The energy-momentum tensor is used in tetrad form to prove that if the nondegeneratemetric of these fields depends only on a single isotropic coordinate, the solutions will describe plane gravitational waves.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 12, No. 4, pp. 20–23, April, 1969.