Spin-induced motion in black hole spacetime

TL;DR

This paper investigates the dynamics of spinning test bodies in black hole spacetimes, deriving exact solutions for circular orbits and analyzing orbital stability and precession effects caused by spin.

Contribution

It provides the first exact solutions for circular orbits in Kerr spacetime without spin truncation and extends perturbation methods to nonplanar orbits with spin effects.

Findings

Exact solutions for circular orbits in Kerr spacetime.

Prediction of the innermost stable circular orbit (ISCO) radius as a function of spin.

Development of nonplanar bound orbits and relativistic precession analysis.

Abstract

Based on the covariant hamiltonian formalism, we study the dynamics of spinning test bodies in the Kerr and Schwarzschild spacetimes. For the first time, we derive the exact solution of circular orbits in the Kerr plane without truncating the spin of the particle or black hole. A large class of noncircular bound orbits has been developed by using the world line perturbation theory. It is found that the spinning body possesses a double frequency, and thus, in addition to the angular shift, the periastron varies radially proportional to the alignment and magnitude of spins. By using the method of stability analysis, we predict the radius of the innermost stable circular orbit (ISCO) as a function of particle and black hole spin. Furthermore, extending the perturbative technique for generic orientation of spin in Schwarzschild spacetime leads to the development of nonplanar bound orbits and the prediction of fully relativistic precessional frequency of the orbital plane.