A study of the neutrino-gravitation interaction

A study of the neutrino-gravitation interaction is made in the framework of Einstein-Dirac coupled equations. Two classes of solutions are obtained, corresponding to two specific physical situations. One cosmological model with expansion is obtained, having neutrinos as the only curvature source; their properties and the parameters which can to characterize the solution as a cosmological model are studied. The second class of solutions corresponds to a naive complete model of a spherically symmetric star emitting neutrinos: the inner region is suposed to be built up of a spherically symmetric distribution of a perfect fluid, bounded in space and which emitts neutrinos; the star matter is considered transparent for neutrinos; the outer region contains only neutrinos and gravitational field. The problem of neutrino compatibility with spherically symmetric gravitational fields is examined. The local conservation laws and the function conditions of the inner and outer solutions in the fluid surface are studied and permit to characterize two kinds of solutions. In one case, the solution describes the neutrino emission phase, with consequent configuration contraction, immediately before the fluid to be completely contained in the interior of the schwarzchild radius, when the neutrino emission and the star contraction stop. The other possibility can correspond to a quasi-stationary configuration, with neutrino emission, where the relativistic equation of radiative equilibrium permits to define the equivalent of 'Radiation pressure' for neutrinos, which acts in the same sense of the gravitational pressure. (L.C.)