# Quasibound states of the Dirac field in Schwarzschild and Reissner-Nordstr\"om black hole backgrounds

## TL;DR

This paper investigates the existence and properties of quasibound states of the massive Dirac field around Schwarzschild and Reissner-Nordström black holes, deriving analytical and numerical energy levels and comparing them to Dirac-Coulomb energies.

## Contribution

It provides analytical expressions for ground state energies and numerical methods for higher states of Dirac quasibound states in black hole backgrounds, including a comparison with Dirac-Coulomb energies.

## Key findings

- Analytical ground state energy expression derived.
- Numerical energies obtained for higher states.
- Good agreement with Dirac-Coulomb energies for small black hole masses.

## Abstract

In this paper, we study the existence of (quasi)bound states in two spacetime geometries describing Schwarzschild and Reissner-Nordstr\"om black holes. For obtaining this type of states we search for discrete quantum modes of the massive Dirac equation in the two geometries. After imposing the quantization condition, an analytical expression for the energy of the ground states is derived. The energy of higher states is then obtained numerically. For very small values of the black hole mass $M$ we compare the energy of the Reissner-Nordstr\"om black hole quasibound state with the Dirac-Coulomb energy and we have found the two to be in good agreement.