Analysis of half-spin particle motion in Reissner-Nordstroem and Schwarzschild fields by means of the method of effective potentials

TL;DR

This paper analyzes the motion of half-spin particles in Schwarzschild and Reissner-Nordstroem gravitational fields using effective potentials, revealing conditions for particle fall and the possibility of bound states inside the horizon.

Contribution

It introduces a detailed analysis of Dirac equations in these fields, identifying unique bound states in extreme Reissner-Nordstroem scenarios.

Findings

Particles generally fall into event horizons in studied cases.

A stationary bound state exists inside the horizon for an extreme Reissner-Nordstroem field.

Most solutions indicate particle infall, with a notable exception for certain bound states.

Abstract

The paper presents the analysis of effective potentials of Dirac equations in Schwarzschild and Reissner-Nordstroem fields. It is shown that in the majority of the explored cases the condition of a particle "fall" to appropriate event horizons is fulfilled. The exception is one of the solutions with normalizable wave functions for the Reissner-Nordstroem extreme field, for which the existence of the stationary bound state of half-spin particles is possible inside the event horizon.