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

Abstract

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 µ the particle mass, we cover dimensionless background spins a/M = (0, ±0.9) and dimensionless particle spins −0.9 ≤ S/µ 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]: we find an unambiguos trend of the PN-prediction towards 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 0.5% in all cases tested. This is close to our fractional numerical accuracy (∼ 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.

Factorization and resummation: A new paradigm to improve gravitational wave amplitudes. III. The spinning test-body terms

“…(i) on the one hand, robust and accurate numerical computations of the energy fluxes from a spinning particle on circular orbits around a Kerr black became available only recently [15][16][17]; (ii) on the other hand, the analytical PN knowledge of the fluxes of a spinning particle around a Kerr black hole was only known at global 2.5PN order [18] and only recently pushed to 3.5PN accuracy [9]. This paper builds on previous works and improves them along two directions: (i) the numerical fluxes of Refs.…”

“…This paper builds on previous works and improves them along two directions: (i) the numerical fluxes of Refs. [16,17] are recomputed, in the time-domain, at an improved accuracy and increasing the number of multipoles. In addition, they are compared with an analogous calculation performed with a completely independent numerical code in the frequency domain, finding excellent consistency between the two methods once the results are linearized in the particle spin; (ii) though we here only consider the case of a spinning particle around a Schwarzschild black hole, the 2.5PN accurate results of Ref.…”

Post-Newtonian templates for binary black-hole inspirals: the effect of the horizon fluxes and the secular change in the black-hole masses and spins

“…For the case of the horizon fluxes emitted from a spinning test-particle on the circular equatorial orbit in Kerr spacetime, the current state of the art is a numerical work by Han [119] as well as an analytical work by Sago and Fujita [116] to 6PN order beyond the quadrupolar fluxes, although Han's result is controversial [120].…”

Hyperboloidal framework for the Kerr spacetime

“…The regularisation factors for the standard Teukoslky radial and angular equations follows straightforward from hyperboloidal gauge degrees of freedom -see eqs. (54) and (55).…”