Publikace ÚTF

We consider a spinning test-body in circular motion around a nonrotating black hole and analyze
different prescriptions for the body’s dynamics. We compare, for the first time, the Mathisson-Papapetrou
formalism under the Tulczyjew spin-supplementary condition (SSC), the Pirani SSC, and the Ohashi-
Kyrian-Semerak SSC, and the spinning particle limit of the effective-one-body 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 coordinate-invariant binding energies, separating
higher-order spin contributions from spin-orbit contributions. The asymptotic gravitational-wave fluxes
produced by the spinning body are computed by solving the inhomogeneous ð2 þ 1ÞD 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 ≡ ðMΩÞ2=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 Ohashi-Kyrian-Semerak and the Pirani SSC the ISCO diverges around
dimensionless spins ∼0.52 and ∼0.94, respectively. In the spin-orbit part of the energetics the deviation
from the Hamiltonian dynamics is largest for the Ohashi-Kyrian-Semerak 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 effective-one-body waveform
models for circularized binaries in the extreme-mass-ratio limit.