Maxwell equations in Schwarzschild black hole with topological defects and the gravitational magnetoelectric effect.

In this study, our primary focus lies in addressing the characteristics of the electromagnetic field tensor within the context of a curved spacetime engendered by a spherically symmetric black hole accompanied by topological defects. Specifically, we scrutinize the Schwarzschild model of a black hole, renowned for its spherically symmetric attributes, while incorporating the additional complexity of a cosmic string traversing the symmetry axis. Our investigation entails deriving the electromagnetic field tensor and subsequently formulating Maxwell vacuum equations, which govern the electric and magnetic fields within this distinctive scenario. Furthermore, we consider a topologically charged spherically symmetric black hole and investigate the same problem within this geometry. The principal findings of our study unveil notable deviations in both the electromagnetic field tensor and the Maxwell equations when compared with outcomes obtained in the conventional Minkowski flat space. Particularly noteworthy is the introduction of a cosmic string and global monopole in our analysis, which introduces supplementary modifications to the results. Moreover, we study the gravitational magnetoelectric effects within these spacetimes' background and analyze the results. [ABSTRACT FROM AUTHOR]