Effect of vacuum polarization on the magnetic fields around a Schwarzschild black hole

Abstract

It is a well known result that the effect of vacuum polarization in gravitational fields will lead to a non-minimal coupling between gravity and electromagnetism. We investigate this phenomenon further by considering the description of static magnetic field around a Schwarzschild black hole. It is found that close to the Schwarzschild horizon the magnetic fields can be strongly modified with respect to both cases of magnetic fields on flat spacetime and magnetic fields minimally coupled on curved spacetime. Under the proper sign of the non-minimal coupling parameter, q, the effective fields can undergo large amplifications. Furthermore, we discuss the physical meaning of the singularities that arise in the considered problem. We conclude by discussing the potential observational effects of vacuum polarization on the magnetic fields. In the case of astrophysical black holes, depending on the value of the coupling parameter, significant modifications of the magnetic near the black hole horizons are possible -which could be used to detect the vacuum polarization effect or at least to put constraints on the values of the coupling parameter. Moreover, we show how the considered effect directly constraints the viability of primordial black holes of sizes smaller than that of the Compton wavelength for the electron, and also impacts the distribution of magnetic fields in the early Universe. arXiv:1809.06054v2 [gr-qc]

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

“…(3), can be used as a suitable approximation in the case of either a galactic magnetic field or a local magnetic field surrounding the Black Hole created by astrophysical processes, when the origin of the magnetic dipole can be understood as being close to the center of the Black Hole, so that both are taken to be situated at r 0. Using this type of magnetic field in the electrody-namic equations of motion obtained from the Lagrangian given by (1), which can be solved by separating the radial and the angular part, B r (r, θ) = B rad (r)Θ(θ), leads to the following equation for the radial component of the magnetic field on the spacetime given by (3), as has been found in [15]:…”

“…This search for signals beyond standard physics is further motivated by the natural expectation that quantum corrections to general relativity and new quantum phenomena should become manifest in strong gravitational fields -and the gravitational fields around Black Holes are the strongest we can currently observe. Following this logic, it was recently proposed in [15] that Black Holes could in principle be used to detect the signatures of non-minimal coupling between gravity and electromagnetic fields, which comes as a result of the quantum effect of vacuum polarization. This is due to the fact that typical astrophysical magnetic fields, for instance the ones characterizing our Galaxy, can become significantly modified near Black Holes due to the arXiv:1908.01888v2 [gr-qc] 15 Oct 2019 vacuum polarization if the value of the non-minimal coupling parameter is large enough.…”

“…Following this logic, it was recently proposed in [15] that Black Holes could in principle be used to detect the signatures of non-minimal coupling between gravity and electromagnetic fields, which comes as a result of the quantum effect of vacuum polarization. This is due to the fact that typical astrophysical magnetic fields, for instance the ones characterizing our Galaxy, can become significantly modified near Black Holes due to the arXiv:1908.01888v2 [gr-qc] 15 Oct 2019 vacuum polarization if the value of the non-minimal coupling parameter is large enough. This fact can be used to detect this effect in future or at least to constrain the potential values of the non-minimal coupling parameter.…”

“…This fact can be used to detect this effect in future or at least to constrain the potential values of the non-minimal coupling parameter. The strongest implications of vacuum polarization in gravitational and magnetic fields are expected in the case of hypothetical primordial Black Holes [15]. This means that the consideration of non-minimal coupling between electromagnetic and gravitational fields due to vacuum polarization is also potentially important for the question of the creation and evolution of cosmological magnetic fields, which is an important question in its own right .…”

“…It should be mentioned here that also other non-minimal couplings between gravity and particle fields have been considered, for example the Higgs-Kretschmann coupling [37][38][39]. In this work we will follow the approach and the results presented in [15] regarding the modification of magnetic fields in the case of asymptotically dipole-like magnetic fields non-minimally coupled to gravity due to the vacuum polarization effect. Using these results we will for the first time study the effects of such a scenario on the motion of charged particles around magnetized SBHs.…”