# Influence of the Vacuum Polarization Effect on the Motion of Charged Particles in the Magnetic Field around a Schwarzschild Black Hole

## TL;DR

This paper investigates how vacuum polarization effects modify magnetic fields around Schwarzschild Black Holes and significantly influence the motion and trajectories of charged particles, potentially serving as observational signatures.

## Contribution

It introduces the impact of vacuum polarization-induced non-minimal coupling on charged particle dynamics near black holes, highlighting new effects on trajectories and magnetic field interactions.

## Key findings

- Vacuum polarization can amplify or suppress magnetic fields near the event horizon.
- Non-minimal coupling affects scattering angles and minimal distances of charged particles.
- Trajectory character (bound or unbound) can depend solely on the coupling strength.

## Abstract

The consequences of the vacuum polarization effect in magnetic fields around a Schwarzschild Black Hole on the motion of charged particles are investigated in this work. Using the weak electromagnetic field approximation, we discuss the non-minimal coupling between magnetic fields and gravity caused by the vacuum polarization and study the equations of motion for the case of a magnetic field configuration which asymptotically approaches a dipole magnetic field. It is shown that the presence of non-minimal coupling can significantly influence the motion of charged particles around Black Holes. In particular, the vacuum polarization effect, leading to strong amplification or suppression of the magnetic field strength around the event horizon (depending on the sign of the coupling parameter), can affect the scattering angle and minimal distance for the electrons moving in the gravitational field of the Black Hole as well as the dependence of these parameters on the asymptotic magnetic field strength, initial distance and the Black Hole mass. It is further demonstrated that the non-minimal coupling between gravity and astrophysical magnetic fields, caused by the vacuum polarization, can cause significant changes of the parameter space corresponding to bound trajectories around the Black Hole. In certain cases, the bounded or unbounded character of a trajectory is determined solely by the presence of non-minimal coupling and its strength. These effects could in principle be used as observational signatures of the vacuum polarization effect and also to constrain the value of the coupling parameter.