Asymptotic gravitational wave fluxes from a spinning particle in circular equatorial orbits around a rotating black hole

We present a new computation of the asymptotic gravitational wave energy fluxes emitted by a spinning particle in circular equatorial orbits about a Kerr black hole. The particle dynamics is computed in the pole-dipole approximation, solving the Mathisson-Papapetrou equations with the Tulczyjew spin-supplementary-condition. The fluxes are computed, for the first time, by solving the $2+1$ Teukolsky equation in the time-domain using hyperboloidal and horizon-penetrating coordinates. Denoting by $M$ the black hole mass and by $\ensuremath{\mu}$ the particle mass, we cover dimensionless background spins $a/M=(0,\ifmmode\pm\else\textpm\fi{}0.9)$ and dimensionless particle spins $\ensuremath{-}0.9\ensuremath{\le}S/{\ensuremath{\mu}}^{2}\ensuremath{\le}+0.9$. Our results span orbits of Boyer-Lindquist coordinate radii $4\ensuremath{\le}r/M\ensuremath{\le}30$; notably, we investigate the strong-field regime, in some cases even beyond the last-stable-orbit. We compare our numerical results for the gravitational wave fluxes with the 2.5th order accurate post-Newtonian (PN) prediction obtained analytically by Tanaka et al. [Phys. Rev. D 54, 3762 (1996)]: we find an unambiguous trend of the PN-prediction toward the numerical results when $r$ is large. At $r/M=30$ the fractional agreement between the full numerical flux, approximated as the sum over the modes $m=1$, 2, 3, and the PN prediction is $\ensuremath{\lesssim}0.5%$ in all cases tested. This is close to our fractional numerical accuracy ($\ensuremath{\sim}0.2%$). For smaller radii, the agreement between the 2.5PN prediction and the numerical result progressively deteriorates, as expected. Our numerical data will be essential to develop suitably resummed expressions of PN-analytical fluxes in order to improve their accuracy in the strong-field regime.

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