Spinning test body orbiting around a Kerr black hole: Comparing spin supplementary conditions for circular equatorial orbits

0561923 - ASÚ 2023 RIV US eng J - Článek v odborném periodiku
Timogiannis, I. - Lukes-Gerakopoulos, Georgios - Apostolatos, Th. A.
Spinning test body orbiting around a Kerr black hole: Comparing spin supplementary conditions for circular equatorial orbits.
Physical Review D. Roč. 106, č. 4 (2022), č. článku 044039. ISSN 2470-0010. E-ISSN 2470-0029
Grant ostatní: AV ČR(CZ) LQ100032102; AV ČR(CZ) Prémie Lumina quaeruntur 2020
Program: Prémie Lumina quaeruntur
Institucionální podpora: RVO:67985815
Klíčová slova: general relativity * quantum cosmology
Obor OECD: Astronomy (including astrophysics,space science)
Impakt faktor: 5, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1103/PhysRevD.106.044039

The worldline of a spinning test body moving in curved spacetime can be provided by the Mathisson-Papapetrou-Dixon equations when its centroid, i.e., its center of mass, is fixed by a spin supplementary condition (SSC).
In the present study, we continue the exploration of shifts between different centroids started in a recently published work [Iason Timogiannis et al., Phys. Rev. D 104, 024042 (2021)., 10.1103/PhysRevD.104.024042], henceforth paper I, for the Schwarzschild spacetime, by examining the frequencies of circular equatorial orbits under a change of the SSC in the Kerr spacetime. In particular, we examine the convergence in the terms of the prograde and retrograde orbital frequencies, when these frequencies are expanded in power series of the spin measure and the centroid of the body is shifted from the Mathisson-Pirani or the Ohashi-Kyrian-Semerák frame to the Tulczyjew-Dixon one. Since in paper I we have seen that the innermost stable circular orbits (ISCOs) hold a special place in this comparison process, we focus on them rigorously in this work. We introduce a novel method of finding ISCOs for any SSC and employ it for the Tulczyjew-Dixon and the Mathisson-Pirani formalisms. We resort to numerical investigation of the convergence between the SSCs for the ISCO case, due to technical difficulties not allowing paper I's analytical treatment. Our conclusion, as in paper I, is that there appears to be a convergence in the power series of the frequencies between the SSCs, which is improved when the proper shifts are taken into account, but there exists a limit in this convergence due to the fact that in the spinning body approximation we consider only the first two lower multipoles of the extended body and ignore all the higher ones.


Trvalý link: https://hdl.handle.net/11104/0334565