Effects of the external magnetic field on the Lense-Thirring precession

In this paper, we study the effects of the external magnetic field on the Lense-Thirring (LT) precession of a test gyroscope attached to an observer in magnetized black hole spacetime. For this, we consider a Kerr-Newman black hole embedded in the external magnetic field. The LT precession of a test gyroscope diverges near the ergosurface and remains finite everywhere outside the ergosurface. It is seen that by increasing the external magnetic field, the LT precession frequency in the region of large r decreases as B increases, while the precession frequency in the region of small r increases as B increases, whereas it increases with increasing the charge of the black hole. The LT precession of a test gyroscope attached to observers moving along the directions close to the polar axis is greater than that of the observer moving in the equatorial plane.