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

Abstract

In a recent work, [Phys. Rev. D. 94, 104010 (2016)], hereafter Paper I, we have numerically studied different prescriptions for the dynamics of a spinning particle in circular motion around a Schwarzschild black hole. In the present work, we continue this line of investigation to 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 ISCO shifts and the frequency parameter $x\equiv (M\Omega {)}^{2/3}$, where $\Omega$ is the orbital frequency and $M$ is the Kerr black hole mass. Then, we solve numerically the inhomogeneous $(2+1)D$ 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 $a=-0.9$ this level of agreement is preserved up to $x<0.1$. For large frequencies ($x\gtrsim 0.1$), 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 $a=-0.9$ case. Instead, in the study of ISCO the negative Kerr parameter $a=-0.9$ results in less discrepancies in comparison with the positive Kerr parameter $a=0.9$.

12 pages, 4 figures, 7 tables

References in corpus (9)

• Hyperboloidal foliations and scri-fixing
• Towards adiabatic waveforms for inspiral into Kerr black holes: I. A new model of the source for the time domain perturbation equation
• A new gravitational wave generation algorithm for particle perturbations of the Kerr spacetime
• Small mass plunging into a Kerr black hole: Anatomy of the inspiral-merger-ringdown waveforms
• Binary black hole coalescence in the extreme-mass-ratio limit: testing and improving the effective-one-body multipolar waveform
• Binary black hole merger gravitational waves and recoil in the large mass ratio limit
• Horizon-absorption effects in coalescing black-hole binaries: An effective-one-body study of the non-spinning case
• Spacelike matching to null infinity
• The antikick strikes back: recoil velocities for nearly-extremal binary black hole mergers in the test-mass limit

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• Spinning particle orbits around a black hole in an expanding background
• Internal structures and circular orbits for test particles
• Stable circular orbits of spinning test particles around accelerating Kerr black hole
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• Geometric studies of the interplay between spin and gravity