Neutrino radiation in spherically-symmetric gravitational fields I. The energy-momentum tensor for the one-neutrino and many-particle neutrino field

The physical situation of a star emitting neutrinos is considered. Some difficulties in the classical theory are mentioned, and a more detailed approach to the properties of neutrino radiation in general relativity is given. The classical theory is here regarded as a one-particle theory, and by summing over many particles propagating in randon radial directions, the energy-momentum tensor of the total radiation field is shown to approximate to the geometrical optics type satisfying other conditions defining its radial and time dependence.