On the stationary axially symmetric Einstein-Weyl field equations

Abstract

The combined gravitational-neutrino field equations in general relativity are solved under the following two assumptions: (i) space-time is stationary axially symmetric and the line element of the metric can be put into a canonical form, (ii) the energy flow vector of the neutrino field is time-like or null for all observers. The resulting metric is uniquely determined and asymptotically non-flat; the Weyl tensor is of Petrov type D, and the Ricci tensor belongs to the class (2T-2S)2 in the Plebanski classification.