# An Integral Representation for the Dirac Propagator in the Reissner-Nordstr\"om Geometry in Eddington-Finkelstein Coordinates

## TL;DR

This paper derives an integral representation for the Dirac propagator in Reissner-Nordström spacetime using Eddington-Finkelstein coordinates, enabling analysis of Dirac particles across the event horizon.

## Contribution

It introduces a novel integral representation of the Dirac propagator in Reissner-Nordström geometry, accounting for horizon-crossing dynamics.

## Key findings

- Provides an explicit integral formula involving separated solutions.
- Describes Dirac particle behavior across the event horizon.
- Applicable up to the Cauchy horizon.

## Abstract

The Cauchy problem for the massive Dirac equation is studied in the Reissner-Nordstr\"om 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.