To Analysis of the Dirac and Majorana Particle Solutions in Schwarzschild Field

Abstract

For massless Dirac particle, general mathematical study of the particle tunneling process through effective potential barrier generated by Schwarzschild black hole background is performed. Results significantly differ for two situations: the first one when a particle falls on the barrier from within and another one when a particle falls from outside. The study is based on the use of eight Frobenius solutions of related second order differential equations with nonregular singularities of the rank two. Mathematical structure of the derived asymptotic relations is exact, however analytical expressions for involved convergent powers series are not known, and further study should be based on numerical summation of the series. The results obyained are valid for massless both Dirac and Majorana particles.