Correct statement of a scattering problem for quantum charged scalar particles on the Reissner-Nordstr\"{o}m black holes

TL;DR

This paper formulates a precise scattering problem for quantum charged scalar particles around Reissner-Nordström black holes, incorporating the black hole's electric field, and presents the S-matrix in a form suitable for practical and numerical analysis.

Contribution

It provides a correct and physically applicable formulation of the scattering problem, including the black hole's electric field, and explores the S-matrix structure for numerical applications.

Findings

S-matrix elements are expressed in a form suitable for numerical computation

The formulation accounts for the black hole's electric field effects

Outlines potential issues for further research

Abstract

We study a correct statement of the scattering problem arising for quantum charged scalar particles on the Reissner-Nordstr\"{o}m black holes when taking into account the own electric field of black hole. The elements of the corresponding S-matrix are explored in the form convenient to physical applications and for applying numerical methods. Some further possible issues are outlined.