Post-Newtonian expansion of fluxes from a scalar charge on an inclined-spherical orbit about a Kerr black hole

TL;DR

This paper derives analytical post-Newtonian expressions for scalar fluxes from a charge in inclined orbits around a Kerr black hole, aiding the modeling of extreme-mass-ratio inspirals.

Contribution

It provides the first 12PN order analytical flux expressions for inclined Kerr orbits, exact in inclination and spin, using the Mano, Suzuki, and Takasugi method.

Findings

Analytical flux expressions match numerical results well in strong-field regions.

Expressions are exact in inclination and spin parameters.

Comparison shows the utility of PN expansions near the black hole.

Abstract

Efforts are underway to accurately model extreme-mass-ratio inspirals for binaries with a spinning (Kerr) primary. At lowest order the adiabatic evolution depends on the radiation fluxes. Fluxes and other self-force quantities can be expanded analytically in post-Newtionian (PN) series allowing the early evolutionary phase to be understood. When it comes to more complicated background geodesic orbits, it proves useful to use the scalar field model problem to guide development and testing of techniques. In this paper, we present analytical expressions for the scalar fluxes from a scalar point-charge in inclined-spherical orbit about a Kerr black hole up to 12PN relative order, with expressions that are exact in terms of the inclination parameter $x$ and black hole spin $a$. The expressions are constructed using the Mano, Suzuki, and Takasugi method of solving the scalar wave equation in a Kerr background. We compare the numerical evaluation of these flux expressions to full numerical ($s=0$) Teukolsky code results, examining their degree of utility as the strong-field region is approached.