Nonequatorial circular orbits of spinning particles in the Schwarzschild–de Sitter background

Plyatsko, Roman; Panat, Volodymyr; Fenyk, Mykola

doi:10.1007/s10714-018-2474-1

Cited by 6 publications

(4 citation statements)

References 41 publications

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“…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: 55%

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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: Tulzcyjew-dixon Sscsupporting

confidence: 55%

“…These helices were considered for long time to be unphysical until their nature was interpreted in [22]. This SSC is quite popular in analytical works [21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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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“…At the same time, it is necessary to study the influence of the spin-gravity coupling on the particle trajectories, especially when its velocity is very high. Various cases of the essentially nongeodesic orbits of a highly relativistic spinning particle in Schwarzschild's field, which follows from the MP equations, are investigated in [16][17][18][19][20][21]. In particular, it is shown that, due to the strong action of the highly relativistic spin-gravity coupling, there are circular orbits of a spinning particle in the Schwarzschild field which significantly differ from the circular orbits of a spinless particle in this field.…”

Section: Role Of the Very High Particle Velocitymentioning

confidence: 99%

On Reaction of a Spinning Particle on the Spacetime Curvature

Plyatsko

Fenyk

2019

Ukr. J. Phys.

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The reaction of a classical (nonquantum) spinning particle on the spacetime curvature according to the Mathisson–Papapetrou equations is analyzed. From the point of view of the observer comoving with the particle in Schwarzschild’s field, this reaction is a reaction on the gravitomagnetic components of the gravitational field. The values of these components significantly depend on the relativistic Lorentz factor calculated by the particle velocity relative to the Schwarzschild mass. As a result, the value of the spinning particle acceleration relative to the geodesic motion is proportional to the second power of the Lorentz factor. At the same time, the intensity of the electromagnetic radiation of a charged spinning particle is proportional to the fourth power of this factor. Some numerical estimates are presented.

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“…The motion of the spinning test particle in the Horndeski theory was also investigated in [61]. Some works have addressed the motion of a spinning test particle with non-zero cosmological constant in Schwarzschild and Kerr-de Sitter spacetimes [62][63][64][65], for which the equilibrium conditions and nonequatorial circular orbits were investigated.…”

Section: Introductionmentioning

confidence: 99%

Motion deviation of test body induced by spin and cosmological constant in extreme mass ratio inspiral binary system

et al. 2019

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The future space-borne detectors will provide the possibility to detect gravitational waves emitted from extreme mass ratio inspirals of stellar-mass compact objects into supermassive black holes. It is natural to expect that the spin of the compact object and cosmological constant will affect the orbit of the inspiral process and hence lead to the considerable phase shift of the corresponding gravitational waves. In this paper, we investigate the motion of a spinning test particle in the spinning black hole background with a cosmological constant and give the order of motion deviation induced by the particle's spin and the cosmological constant by considering the corresponding innermost stable circular orbit. By taking the neutron star or kerr black hole as the small body, the deviations of the innermost stable circular orbit parameters induced by the particle's spin and cosmological constant are given. Our results show that the deviation induced by particle's spin is much larger than that induced by cosmological constant when the test particle locates not very far away from the black hole, the accumulation of phase shift during the inspiral from the cosmological constant can be ignored when compared to the one induced by the particle's spin. However when the test particle locates very far away from the black hole, the impact from the cosmological constant will increase dramatically. Therefore the accumulation of phase shift for the whole process of inspiral induced by the cosmological constant and the particle's spin should be handled with caution. a

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Nonequatorial circular orbits of spinning particles in the Schwarzschild–de Sitter background

Cited by 6 publications

References 41 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

On Reaction of a Spinning Particle on the Spacetime Curvature

Motion deviation of test body induced by spin and cosmological constant in extreme mass ratio inspiral binary system

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