An Integral Representation for the Dirac Propagator in the Reissner-Nordström Geometry in Eddington-Finkelstein Coordinates

The Cauchy problem for the massive Dirac equation is studied in the Reissner-Nordström geometry in horizon-penetrating Eddington-Finkelstein-type coordinates. We derive an integral representation for the Dirac propagator involving the solutions of the ordinary differential equations which arise in the separation of variables. Our integral representation describes the dynamics of Dirac particles outside and across the event horizon, up to the Cauchy horizon.