Gyroscope precession along bound equatorial plane orbits around a Kerr black hole

TL;DR

This paper analyzes the precession behavior of a test gyroscope on stable equatorial orbits around a Kerr black hole, providing insights into the geometric and physical aspects of gyroscopic precession in curved spacetime.

Contribution

It offers a detailed analysis of gyroscope precession in Kerr spacetime, including the precession angular velocity and angle increment, with a novel geometric interpretation using the Marck frame and Killing-Yano form.

Findings

Derived explicit expressions for precession angular velocity.

Calculated the precession angle after one orbital period.

Connected the precession to geometric properties of spacetime.

Abstract

The precession of a test gyroscope along stable bound equatorial plane orbits around a Kerr black hole is analyzed and the precession angular velocity of the gyro's parallel transported spin vector and the increment in precession angle after one orbital period is evaluated. The parallel transported Marck frame which enters this discussion is shown to have an elegant geometrical explanation in terms of the electric and magnetic parts of the Killing-Yano 2-form and a Wigner rotation effect.