Spinning test body orbiting around a Schwarzschild black hole: Circular dynamics and gravitationalwave fluxes
Abstract
We consider a spinning testbody in circular motion around a nonrotating black hole and analyze different prescriptions for the body's dynamics. We compare, for the first time, the MathissonPapapetrou formalism under the Tulczyjew spinsupplementary condition (SSC), the Pirani SSC, and the OhashiKyrianSemerak SSC, and the spinning particle limit of the effectiveonebody Hamiltonian of Damour and Nagar [Phys. Rev. D 90, 044018 (2014).]. We analyze the four different dynamics in terms of the innermost stable circular orbit (ISCO) shifts and in terms of the coordinateinvariant binding energies, separating higherorder spin contributions from spinorbit contributions. The asymptotic gravitationalwave fluxes produced by the spinning body are computed by solving the inhomogeneous (2 +1 )D Teukolsky equation and contrasted for the different cases. For small orbital frequencies Ω , all the prescriptions reduce to the same dynamics and the same radiation fluxes. For large frequencies, x ≡(M Ω )2^{/3}>0.1 , where M is the black hole mass, and especially for positive spins (aligned with the orbital angular momentum) a significant disagreement between the different dynamics is observed. The ISCO shifts can differ by up to a factor of 2 for large positive spins; for the OhashiKyrianSemerak and the Pirani SSC the ISCO diverges around dimensionless spins ̃0.52 and ̃0.94 , respectively. In the spinorbit part of the energetics the deviation from the Hamiltonian dynamics is largest for the OhashiKyrianSemerak SSC; it exceeds 10% for x >0.17 . The Tulczyjew and the Pirani SSCs are compatible across almost the whole spin and frequency range. Our results will have direct applications in including spin effects in effectiveonebody waveform models for circularized binaries in the extrememassratio limit.
 Publication:

Physical Review D
 Pub Date:
 November 2016
 DOI:
 10.1103/PhysRevD.94.104010
 arXiv:
 arXiv:1609.00356
 Bibcode:
 2016PhRvD..94j4010H
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 Few corrections were added after the publication