On plane wave-like solutions of non-symmetric unified field theories (Q1249350)

Non-symmetric unified field theories of Einstein (1951), Bonnor (1954) and Schrödinger (1950) are treated in a unified way in the space-time \[ des^2 = - Adx^2 - Bdy^2 - (1 - E)dz^2 - 2Edzdt + (1 +E)dt^2, \] \(A=A(z,t),\;B=B(z,t),\;E=E(x,y,z,t)\). The solutions and various cases are clearly discussed. Physically, the solutions have plane wave-like character. Further it is obtained (to appear in Tensor in 1979) that the energy carried by the gravitational waves in all Peres space-times which is characterized by (i) it admits a parallel null vector field and (ii) it is a gravitational null field, is not zero as known earlier. This space-time is such an example.