On the black holes in external electromagnetic fields

TL;DR

This paper develops a mathematical framework for constructing axially symmetric black holes and naked singularities immersed in external electromagnetic fields, expanding the theoretical understanding of such configurations.

Contribution

It introduces a method to construct axially symmetric black holes and singularities in external electromagnetic fields, enhancing the mathematical theory of gravitational-electromagnetic interactions.

Findings

Method for constructing black holes in external fields

Framework for axially symmetric solutions

Extension to naked singularities

Abstract

This preprint mainly reflects the new chapter we are prepearing for the second edition of our book "Gravitational Solitons" (V. Belinski and E. Verdaguer). However, here it is written in the form of more or less self-consistent paper dedicated to the mathematical theory of black holes immersed in the external electromagnetic field. The purpose of this development is to describe the procedure by which one can construct a number of axially symmetric black holes or naked singularities arranged along the symmetry axis and immersed in an (also axially symmetric) external electromagnetic field.