Spin precession in magnetized Kerr spacetime

We present an exact analytical investigation of spin precession for a test gyroscope in the magnetized Kerr spacetime—an exact electrovacuum solution to the Einstein-Maxwell equations. Our approach accommodates arbitrary magnetic field strengths, enabling a unified treatment across both weak and ultrastrong field regimes. The analysis reveals distinct spin precession behaviors near rotating collapsed objects, which differ characteristically between black holes and naked singularities, offering a potential observational means to differentiate them. The external magnetic field induces a nontrivial modification of the precession frequency through its interaction with the spacetime’s gravitoelectromagnetic structure. In the weak-field limit, magnetic fields generally reduce the precession rate, though the effect depends sensitively on the motion and orientation of the test gyro close to the collapsed object. As a special case, we show that in the presence of magnetic fields, the spin precession frequency due to gravitomagnetic effect acquires a long-range 1=r (where r is the distance from the central object to the test gyro) correction in contrast to the standard 1=r³ falloff. In addition, we obtain the exact geodetic precession (gravitoelectric effect) frequency for a gyroscope in magnetized Schwarzschild spacetime, showing that the magnetic field enhances (∝ r¹=²) geodetic precession in contrast to the standard 1=r⁵=² falloff. Our results provide observationally testable predictions relevant for black holes in strong magnetic environments, including those possibly realized near magnetars or in the early universe. In particular, the strong-field behavior of spin precession could have important implications for transmuted black holes formed via collapse or mergers of magnetized progenitors in both astrophysical and cosmological contexts.