Neutrinos in gravitational collapse: The Dirac formalism

Abstract

The massless Dirac equations for the neutrino are studied in the background geometry relevant to a gravitational collapse, i.e., a Friedmann dust interior matched onto a Schwarzschild exterior. The interior normal modes are obtained and continued consistently across the collapsing surface into the exterior. This yields the expected spectral shifts quite naturally in addition to the phenomenon of backward emission. The complete exterior modes are obtained by matching solutions at the Schwarzschild barrier. The asymptotic transmission coefficient is computed, and this includes in addition to the effects of gravitational collapse the effects of the exterior potential barrier.