Asymptotic gravitational wave fluxes from a spinning particle in circular equatorial orbits around a rotating black hole
Abstrakt
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 mu the particle mass, we cover dimensionless background spins a/M = (0, +/- 0.9) and dimensionless particle spins -0.9 <= S/mu(2) <= +0.9.
Our results span orbits of Boyer-Lindquist coordinate radii 4 <= r/M <= 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 less than or similar to 0.5% in all cases tested. This is close to our fractional numerical accuracy (similar to 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.