On the Non-Minimal Coupling of Magnetic Fields with Gravity in Schwarzschild Spacetime

TL;DR

This paper investigates how non-minimal coupling between electromagnetism and gravity, motivated by quantum effects, alters magnetic fields around Schwarzschild black holes, with potential observational implications for astrophysics.

Contribution

It provides a detailed analysis of magnetic field modifications due to non-minimal coupling in Schwarzschild spacetime, including effects on field strength and direction near black holes.

Findings

Magnetic fields can be enhanced or suppressed depending on the coupling sign.

The magnetic field direction can change near the black hole horizon.

Observations of synchrotron radiation could constrain the coupling parameter.

Abstract

In this work we study the effects of non-minimal coupling between electromagnetism and gravity, which are motivated by quantum effects such as vacuum polarization. We investigate the modification of both asymptotically dipole and uniform magnetic fields around a Schwarzschild black hole that come as the result of non-minimal coupling. While in both cases the magnetic field gets enhanced or suppressed with respect to the case of minimal coupling, depending on the sign of non-minimal coupling parameter, in the case of a background uniform magnetic field the direction of the magnetic field also alters in the vicinity of the black hole horizon. We have discussed the possible astrophysical and cosmological sources for which the vacuum polarization may be at play, while also discussing the observational effects, in particular the possibility of synchrotron radiation from the vicinity of a black hole. We conclude that such observations could be used to constrain the value of the non-minimal coupling parameter.