Spin Precession in magnetized Kerr spacetime

TL;DR

This paper provides an exact analytical study of spin precession in magnetized Kerr spacetime, revealing how magnetic fields influence precession rates and behaviors near compact objects, with implications for astrophysical observations.

Contribution

It offers a unified analytical framework for spin precession in magnetized Kerr spacetime across all magnetic field strengths, including new effects of magnetic fields on precession.

Findings

Magnetic fields modify the precession frequency, especially near compact objects.

In weak fields, magnetic effects generally reduce precession rates.

Magnetic fields introduce a long-range $1/r$ correction to gravitomagnetic precession.

Abstract

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 ultra-strong 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 $1/r^3$ 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 ($\propto r^{1/2}$) geodetic precession in contrast to the standard $1/r^{5/2}$ 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.