A new approach to the calculation of extreme-mass-ratio inspirals with a spinning secondary

Abstract

Extreme-mass-ratio inspirals (EMRIs) are among the most promising sources for future space-based gravitational-wave (GW) detectors, such as LISA. To fully leverage the scientific potential, the GW templates required for parameter estimation must be modeled with high accuracy for eccentric precessing binary systems with nonzero spins. This work introduces a practical and efficient framework for incorporating the effects of secondary spin in fully generic, eccentric, and offequatorial EMRIs to the first postadiabatic order. We utilize recently found analytic solutions for the trajectories of spinning bodies in Kerr spacetime to significantly simplify the calculation of the corresponding asymptotic GW fluxes. Furthermore, thanks to the recently proven flux-balance laws, we show how to express the rates of change of the constants of motion, including the Carter-Rüdiger constant, using asymptotic Teukolsky amplitudes and purely geodesic functions that are already established in the literature. Finally, we show how this framework performs in the case of nearly-spherical inspirals and demonstrate that the resulting spin-induced phase shifts are gauge independent. A Wolfram Mathematica implementation of the code developed in this work is publicly available in the KerrSpinningFluxes package.

Figures (5)

• Figure 1: Linear parts of the frequencies $\Omega_i^1$ in different spin gauges: fixed shifted constants $\boldsymbol{\Tilde{C}}$, fixed constants $\boldsymbol{C}$, fixed turning points $\boldsymbol{p}$, and fixed actions $\boldsymbol{J}$. The orbital parameters are $a=0.95M$, $e=0.5$, $x=0.5$.
• Figure 2: Linear parts of the infinity amplitudes (top) and total energy fluxes (bottom) calculated using the analytical trajectory and the trajectory calculated using the Drummond's and Hughes' method with different numbers of Fourier modes $k^s_{\text{max}}$. $a=0.9M$, $p=12$, $e=0.2$, $x=0.5$, $l=2$, $m=2$, $n=0$.
• Figure 3: Absolute difference of linear parts of energy fluxes. $a=0.9M$, $p=12$, $e=0.2$, $x=0.5$, $l=2$, $m=2$, $n=0$.
• Figure 4: Phase differences between inspirals calculated in the fixed $\boldsymbol{\Tilde{C}}$ gauge and fixed turning points gauge from Skoupy:2025b.
• Figure 5: Isofrequency line in the $(p,e)$ plane for different Kerr parameters $a$ and $x=0.5$ (left) and for different inclinations $x$ and $a=0.95M$ (right).