Geometrical locus of massive test particle orbits in the space of physical parameters in Kerr space-time

TL;DR

This paper analytically characterizes the geometric locus of all possible bound orbits, including spherical and eccentric ones, in Kerr space-time, providing insights into their parameter relationships and potential orbital transitions.

Contribution

It introduces an analytical determination of the geometric locus of all bound orbits in Kerr space-time, encompassing both spherical and eccentric trajectories.

Findings

Derived the geometric locus of all bound orbits in Kerr space-time.

Analyzed the influence of black hole angular momentum on orbit properties.

Provided a tool to assess continuous orbital parameter changes.

Abstract

Gravitational radiation of binary systems can be studied by using the adiabatic approximation in General Relativity. In this approach a small astrophysical object follows a trajectory consisting of a chained series of bounded geodesics (orbits) in the outer region of a Kerr Black Hole, representing the space time created by a bigger object. In our paper we study the entire class of orbits, both of constant radius (spherical orbits), as well as non-null eccentricity orbits, showing a number of properties on the physical parameters and trajectories. The main result is the determination of the geometrical locus of all the orbits in the space of physical parameters in Kerr space-time. This becomes a powerful tool to know if different orbits can be connected by a continuous change of their physical parameters. A discussion on the influence of different values of the angular momentum of the hole is given. Main results have been obtained by analytical methods.