Ghost neutrinos in general relativity

An exact solution to the Einstein-Dirac equations is presented for a static, plane-symmetric spacetime generated by neutrinos. We find the neutrino field to be nonzero and correspond to a neutrino current along the symmetry axis of the space. The neutrinos yield a zero energy-momentum tensor and therefore the gravitational field is exactly the same as for the vacuum case. A comparison with other solutions is presented along with a discussion of the possible physical significance of this "ghost neutrino" field.