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

2017; American Physical Society; Volume: 96; Issue: 6 Linguagem: Inglês

10.1103/physrevd.96.064051

2470-0037

Georgios Lukes-Gerakopoulos, Enno Harms, Sebastiano Bernuzzi, Alessandro Nagar,

Black Holes and Theoretical Physics

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 $x\ensuremath{\equiv}(M\mathrm{\ensuremath{\Omega}}{)}^{2/3}$, where $\mathrm{\ensuremath{\Omega}}$ is the orbital frequency and $M$ is the Kerr black hole mass. Then, we solve numerically the inhomogeneous $(2+1)D$ 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 $a=\ensuremath{-}0.9$, this level of agreement is preserved up to $x<0.1$. For large frequencies ($x\ensuremath{\gtrsim}0.1$), 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 $a=\ensuremath{-}0.9$ case. Instead, in the study of ISCO, the negative Kerr parameter $a=\ensuremath{-}0.9$ 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 $\ensuremath{\sigma}<0.25$ ($\ensuremath{\sigma}$ denotes the test body's spin), while for the Pirani SSC, ISCOs could be found only for $\ensuremath{-}0.68<\ensuremath{\sigma}<0.64$. For $a=\ensuremath{-}0.9$, for the Ohashi-Kyrian-Semerak SSC, ISCOs could be found for $\ensuremath{\sigma}<0.721$.