Post-Newtonian expansion of gravitational energy and angular momentum fluxes: inclined spherical orbits about a Kerr black hole

TL;DR

This paper derives analytical post-Newtonian expressions for energy and angular momentum fluxes from a point mass on inclined spherical orbits around a Kerr black hole, valid up to 12PN order, and validates them against numerical data.

Contribution

It provides the first 12PN analytical flux formulas for inclined orbits around Kerr black holes using the Mano, Suzuki, and Takasugi method.

Findings

Validated analytical flux expressions against numerical calculations.

Characterized the dependence of PN expansions on inclination and spin.

Extended the accuracy of flux calculations to 12PN order.

Abstract

We present analytical expressions for the fluxes of energy and angular momentum from a point mass on an inclined spherical orbit about a Kerr black hole. The expressions are obtained using the method of Mano, Suzuki and Takasugi to construct analytical solutions of the Teukolsky equation, and are given as post-Newtonian expansions valid through 12PN, with arbitrary values for the inclination parameter $x$ and black hole spin $a$. We characterize the structure of the PN expansions in terms of their dependence on $x$ and $a$, and we validate our results against numerical calculations.