Aschenbach effect for spinning particles in Kerr spacetime

Khodagholizadeh, Jafar; Perlick, Volker; Vahedi, Ali

doi:10.1103/physrevd.102.024021

Cited by 8 publications

(15 citation statements)

References 21 publications

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“…As a second crosscheck, record that, Eq. ( 28) is identical to the one derived in [31], when a → 0. Additionally, the physically acceptable solutions (corotating and counterrotating) are chosen so that Ω ± ∝ ±r − 3 2 , for a non-spinning body.…”

Section: Mathisson-pirani Sscsupporting

confidence: 77%

“…The quadratic equation for the orbital frequency of an extended, spinning, test body, in the Schwarzschild black hole limit is reduced to: (24) which coincides with the expression presented in [31], when the Kerr parameter is set to zero. The solutions of such an equation and the behaviour of its discriminant, have been thoroughly examined by numerous authors and in more general contexts (a = 0).…”

Section: Tulzcyjew-dixon Sscsupporting

confidence: 54%

“…Both numerical and semianalytic methods, based on the concept of effective potentials [5,17,28,29], have been in development since the pioneering work of Rasband [30]. Khodagholizadeh et al [31], on the other hand, followed a more straightforward and purely analytical approach, by evaluating all the non vanishing components of the MPD equations for a Kerr background under any SSC, but obtained results for only the TD and the MP conditions. In this section, we generalize this analytical procedure for arbitrary, stationary, axisymmetric spacetimes, with reflection symmetry (SAR spacetimes); we then focus on TD, MP and OKS SSCs and use Schwarzschild spacetime as a specific example for each SSC.…”

Section: Circular Equatorial Orbitsmentioning

confidence: 99%

“…Additionally, the physically acceptable solutions (corotating and counterrotating) are chosen so that Ω ± ∝ ±r − 3 2 , for a non-spinning body. An extended discussion concerning the generic roots of polynomial ( 28) can be found in [21], while the explicit expressions of the roots can be found in [21] and a Taylor expansion in [31].…”

Section: Mathisson-pirani Sscmentioning

confidence: 99%

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Spinning test body orbiting around a Schwarzschild black hole: Comparing Spin Supplementary Conditions for Circular Equatorial Orbits

Timogiannis,

Lukes-Gerakopoulos,

Apostolatos

2021

Preprint

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The Mathisson-Papapetrou-Dixon (MPD) equations describe the motion of an extended test body in general relativity. This system of equations, though, is underdetermined and has to be accompanied by constraining supplementary conditions, even in its simplest version, which is the pole-dipole approximation corresponding to a spinning test body. In particular, imposing a spin supplementary condition (SSC) fixes the center of the mass of the spinning body, i.e. the centroid of the body. In the present study, we examine whether characteristic features of the centroid of a spinning test body, moving in a circular equatorial orbit around a massive black hole, are preserved under the transition to another centroid of the same physical body, governed by a different SSC. For this purpose, we establish an analytical algorithm for deriving the orbital frequency of a spinning body, moving in the background of an arbitrary, stationary, axisymmetric spacetime with reflection symmetry, for the Tulzcyjew-Dixon, the Mathisson-Pirani and the Ohashi-Kyrian-Semerák SSCs. Then, we focus on the Schwarzschild black hole background and a power series expansion method is developed, in order to investigate the discrepancies in the orbital frequencies expanded in power series of the spin among the different SSCs. Lastly, by employing the fact that the position of the centroid and the measure of the spin alters under the centroid's transition, we impose proper corrections to the power expansion of the orbital frequencies, which allows to improve the convergence between the SSCs. Our concluding argument is that when we shift from one circular equatorial orbit to another in the Schwarzschild background, under the change of a SSC, the convergence between the SSCs holds only up to certain powers in the spin expansion, and it cannot be achieved for the whole power series.

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Section: Mathisson-pirani Sscsupporting

confidence: 77%

Section: Tulzcyjew-dixon Sscsupporting

confidence: 54%

Section: Circular Equatorial Orbitsmentioning

confidence: 99%

Section: Mathisson-pirani Sscmentioning

confidence: 99%

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Spinning test body orbiting around a Schwarzschild black hole: Comparing Spin Supplementary Conditions for Circular Equatorial Orbits

Timogiannis,

Lukes-Gerakopoulos,

Apostolatos

2021

Preprint

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“…O(σ 4 ) Ω4,TD (r, â) Ω4,MP (r, â) Ω4,OKS (r, â) sults note that when â vanishes the columns of Table I in Paper I are recovered, while the Ω± of Table III are also valid in the geodesic limit. We would like to mention at this point that a similar analysis is given in [36],…”

Section: ωNmentioning

confidence: 66%

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

2021

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The worldline of a spinning test body moving in curved spacetime can be provided by the Mathisson-Papapetrou-Dixon (MPD) 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 [Phys. Rev. D 104, 024042 (2021)], 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 an analytical method of finding ISCOs for any SSC and employ it for the Tulczyjew-Dixon and the Mathisson-Pirani formalisms. However, at the end we resort to numerical investigation of the convergence between the SSCs for the ISCO case, due to technical difficulties with the Ohashi-Kyrian-Semerák SSC. 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.

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Aschenbach effect and circular orbits in static and spherically symmetric black hole backgrounds

Wei,

Liu

2024

Physics of the Dark Universe

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Aschenbach effect for spinning particles in Kerr spacetime

Cited by 8 publications

References 21 publications

Spinning test body orbiting around a Schwarzschild black hole: Comparing Spin Supplementary Conditions for Circular Equatorial Orbits

Spinning test body orbiting around a Schwarzschild black hole: Comparing Spin Supplementary Conditions for Circular Equatorial Orbits

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

Aschenbach effect and circular orbits in static and spherically symmetric black hole backgrounds

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