Effect of rotation and magnetic field in the gyroscopic precession around a neutron star

General relativistic effects are essential in defining the spacetime around massive astrophysical objects. The effects can be captured using a test gyro. If the gyro rotates at some fixed orbit around the star, then the gyro precession frequency captures all the general relativistic effects. In this article, we calculate the overall precession frequency of a test gyro orbiting a rotating neutron star or a rotating magnetar. We find that the gyro precession frequency diverges as it approaches a black hole, whereas, for a neutron star, it always remains finite. For a rotating neutron star, a prograde motion of the gyro gives a single minimum, whereas a retrograde motion gives a double minimum. We also find that the gyroscope precession frequency depends on the star’s mass and rotation rate. Depending on the magnetic field configuration, we find that of the precession frequency of the gyro differs significantly inside the star; however, outside the star, the effect is not very prominent. Also, the gyro precession frequency depends more significantly on the star’s rotation rate than its magnetic field strength