Solution for "geodesic" motion of a Schwarzschild black hole along a magnetic field in AdS2 x S2 space-time

TL;DR

This paper presents an exact solution describing a Schwarzschild black hole undergoing geodesic oscillations within a magnetic universe modeled by AdS2 x S2 space-time, revealing complex interactions with gravitational and electromagnetic fields.

Contribution

It provides the first exact Einstein-Maxwell solution for a black hole with initial boost in a Bertotti-Robinson magnetic universe, illustrating geodesic oscillatory motion.

Findings

Black hole exhibits finite initial boost and oscillates geodesically.

Interaction with magnetic and gravitational fields influences black hole motion.

Solution enhances understanding of black hole dynamics in magnetic universes.

Abstract

The exact solution of Einstein - Maxwell equations for a Schwarzschild black hole immersed in the static spatially homogeneous AdS${}^2\times\mathbb{S}^2$ space-time of Bertotti-Robinson magnetic universe is presented. In this solution, the black hole possesses a finite initial boost in the direction of the magnetic field and performs a "geodesic" oscillating motion interacting with the background gravitational and electromagnetic fields.