Observables of a test-mass along an inclined orbit in a post-Newtonian approximated Kerr spacetime to leading-order-quadratic-in-spin

TL;DR

This paper derives the orbital observables of a test-mass in a Kerr spacetime including quadratic-in-spin effects, expanding the gravitational field to second post-Newtonian order, and introduces new canonical variables for analysis.

Contribution

It presents a novel analytical framework for orbital motion in a Kerr spacetime with quadratic spin effects using action-based methods.

Findings

Derived orbital period, periastron advance, and orbital plane precession including quadratic spin effects.

Introduced new canonical variables for analyzing orbits in Kerr spacetime.

Expanded the Kerr metric to second post-Newtonian order with spin terms.

Abstract

The orbital motion is derived for a non-spinning test-mass in the relativistic, gravitational field of a rotationally deformed body not restricted to the equatorial plane or spherical orbit. The gravitational field of the central body is represented by the Kerr metric, expanded to second post-Newtonian order including the linear and quadratic spin terms. The orbital period, the intrinsic periastron advance, and the precession of the orbital plane are derived with the aid of novel canonical variables and action-based methods.