Adiabatic Evolution of three 'Constants' of Motion for Greatly Inclined Orbits in Kerr spacetime

TL;DR

This paper develops a new formulation to compute the evolution of the Carter constant for particles in Kerr spacetime, especially for highly inclined orbits, extending previous methods without small inclination assumptions.

Contribution

We present a refined and extended method to calculate the adiabatic evolution of the Carter constant without relying on small inclination angle expansions.

Findings

New formulation for Carter constant evolution

Applicable to highly inclined orbits in Kerr spacetime

Improved computational efficiency

Abstract

General orbits of a particle of small mass $\mu$ around a Kerr black hole of mass $M$ are characterized by three parameters: the energy, the angular momentum and the Carter constant. The time-averaged rates of change of the energy and the angular momentum can be obtained by computing the corresponding fluxes of gravitational waves emitted by the particle. By contrast, the time-averaged rate of change of the Carter constant cannot be expressed as a flux of gravitational waves. Recently a method to compute this rate of change was proposed by Mino, and we refined it into a simplified form. In this paper we further extend our previous work to give a new formulation without the aid of expansion in terms of a small inclination angle.