# Magnetized Black Holes in an External Gravitational Field

## TL;DR

This paper presents exact solutions for magnetized black holes in external gravitational fields, analyzing their thermodynamics and effects of external potentials, including the Meissner effect in extremal cases.

## Contribution

It introduces a new family of solutions describing magnetized black holes influenced by external gravitational and magnetic fields, extending previous models to include combined external potentials.

## Key findings

- External fields affect black hole properties distinctly.
- Static solutions show factorized influence of external fields.
- Extremal rotating solutions exhibit the Meissner effect in zero-charge limit.

## Abstract

We obtain a family of exact solutions describing magnetized black holes in an external gravitational field. Locally the solutions can be interpreted as representing the near-horizon region of a black hole, which interacts with a surrounding matter distribution producing a strong magnetic field. Thus, the solutions reflect the influence of both a gravitational and an electromagnetic external potential in the strong field regime. The static members in the family are generalizations of the Schwarzschild solution in the described environment, while the rotating ones generalize the magnetized Reissner-Nordstr\"om solution when the influence of an external gravitational source is also taken into account. Technically, the solutions are obtained by means of a Harrison transformation. We examine the thermodynamical properties of the solutions, and compare them with the corresponding isolated black holes, and with the particular cases when the interaction with only one of the external potentials is taken into account. For the static black holes the influence of the external gravitational and magnetic fields is factorized in a sense, both affecting different properties, and leaving the rest intact. For the rotating solutions the external gravitational and magnetic fields are coupled through the conditions for avoiding conical singularities. The Meissner effect is observed for extremal rotating solutions only in the zero-charge limit, similar to the magnetized Reissner-Nordstr\"om black hole.