Spinning test body orbiting around a Kerr black hole: Circular dynamics and gravitational-wave fluxes

In a recent work [Phys. Rev. D 94, 104010 (2016)], hereafter Paper I, we numerically studied different prescriptions for the dynamics of a spinning body in circular motion around a Schwarzschild black hole. In the present work, we continue this line of investigation by studying the rotating Kerr black hole. We consider the Mathisson-Papapetrou formalism under three different spin-supplementary conditions (SSC), the Tulczyjew SSC, the Pirani SSC, and the Ohashi-Kyrian-Semerak SSC, and analyze the different circular dynamics in terms of the innermost stable circular orbit (ISCO) shifts and the frequency parameter x (M Omega)(2/3,) where Omega is the orbital frequency and M is the Kerr black hole mass. Then, we solve numerically the inhomogeneous (2 + 1) Teukolsky equation to contrast the asymptotic gravitational wave fluxes for the three cases. Our central observation made in Paper I for the Schwarzschild limit is found to hold true for the Kerr background; the three SSCs reduce to the same circular dynamics and the same radiation fluxes for small frequency parameters, but differences arise as x grows close to the ISCO. For a positive Kerr parameter a = 0.9, the energy fluxes mutually agree with each other within a 0.2% uncertainty up to x < 0.14, while for a = -0.9, this level of agreement is preserved up to x < 0.1. For large frequencies (x. 0.1), however, the spin coupling of the Kerr black hole and the spinning body results in significant differences of the circular orbit parameters and the fluxes, especially for the a = -0.9 case. Instead, in the study of ISCO, the negative Kerr parameter a = -0.9 results in fewer discrepancies in comparison with the positive Kerr parameter a = 0.9. As a side result, we mention that, apart from the Tulczyew SSC, ISCOs could not be found over the full range of spins; for a = 0.9, for the Ohashi-Kyrian-Semerak SSC, ISCOs could be found only for sigma < 0.25 (sigma denotes the test body's spin), while for the Pirani SSC, ISCOs could be found only for -0.68 < sigma < 0.64. For a = -0.9, for the Ohashi-Kyrian-Semerak SSC, ISCOs could be found for sigma < 0.721.