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

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>x</a:mi> </a:mrow> </a:math> and black hole spin <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>a</c:mi> </c:math> . 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 ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>s</e:mi> <e:mo>=</e:mo> <e:mn>0</e:mn> </e:math> ) eukolsky code results, examining their degree of utility as the strong-field region is approached.