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

Jezreel C. Castillo1, Charles R. Evans1,2, Chris Kavanagh2, Jakob Neef2, Barry Wardell2, and Adrian Ottewill2

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Phys. Rev. D 112, 104001 – Published 3 November, 2025

DOI: https://doi.org/10.1103/n4dl-zm7p

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-Newtonian (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.

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Information

Phys. Rev. D 112, 104001– Published 3 November, 2025
  • Received 18 July 2025
  • Accepted 1 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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