Influence of the vacuum polarization effect on the motion of charged particles in the magnetic field around a Schwarzschild black hole

Abstract

The consequences of the vacuum polarization effect in magnetic fields around a Schwarzschild Black Hole (SBH) 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.

On Non-minimal Coupling of Magnetic Field with Gravity in the Schwarzschild Spacetime

“…We should compare the results of [3,4] with the present work. Although the main conclusions and the qualitative behaviour is the same in these previous works to the one we found in this study, there are still some quantitative differences present.…”

“…Although the main conclusions and the qualitative behaviour is the same in these previous works to the one we found in this study, there are still some quantitative differences present. Though far from the event horizon, in the asymptotically flat region, both this presentation and that of [3,4] don't differ significantly, and both have the same typical dipole form(B r (r, θ) = 2const.×cos θ/r 3 and B θ (r, θ) = const. × sin θ/r 3 ), but near the event horizon they differ.…”

“…At this point we need to stress the most important physical approximations which we take in our study, which were also assumed in earlier works [3,4]. We first assume that magnetic fields are weak enough so that the their effect on the spacetime stays negligible, and can therefore still be described by the Schwarzschild metric.…”

“…In [3] it was proposed that the signatures of nonminimal coupling between electromagnetism and gravity could be in principle observed, or at least constrained, by studying the magnetic fields around the event horizons of black holes and that the same effect could be used for constraining the sizes of primordial black holes. With this aim, the problem of modification of magnetic fields due to the vacuum polarization effect around the Schwarzschild black hole was for the first time studied in [3] and the consequences for the orbits of charged particles around such black holes were for the first time studied in [4]. In this work we try to further develop the investigation of this topic.…”

Geodesic Circular Orbits Sharing the Same Orbital Frequencies in the Black String Spacetime

“…These observations opened a qualitatively new stage to reveal black hole's unknown properties and test remarkable nature of the background geometry around black hole's horizon irrespective of the fact that there are still fundamental problems that general relativity faces, i.e., the occurrence of singularity, spacetime quantization, etc. In this framework, the motion of test particles in the strong gravitational field regime has been a productive field of study for several years [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. On the other hand, there is an extensive body of work devoted to understand the nature of radiative inspirals around black holes as a source of gravitational waves and binary systems [20][21][22][23][24][25][26][27][28].…”