Clock effect due to gravitational spin–orbit coupling

Faruque, Syed Badiuzzaman

doi:10.1016/j.physleta.2006.06.046

Cited by 11 publications

(18 citation statements)

References 13 publications

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“…(48). This constitutes a generalization of previous results [18,19,34] that involved onlyŝ Ĵ 1. Imagine a spinning particle revolving around a Kerr source in accordance with Eqs.…”

Section: Gravitomagnetic Clock Effectsupporting

confidence: 85%

“…As noted in Ref. [34], a similar result has been obtained in the treatment of a Dirac particle in the Schwarzschild field [42 -45].…”

supporting

confidence: 79%

“…(B4), the spin-orbit term is a small relativistic correction to the Newtonian dynamics and turns out to be the source of the spin-dependence of the clock effect [34]. It follows from Hamilton's equations of motion for Eq.…”

mentioning

confidence: 99%

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Dynamics of extended spinning masses in a gravitational field

2006

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We develop a first-order approximation method for the influence of spin on the motion of extended spinning test masses in a gravitational field. This approach is illustrated for approximately circular equatorial motion in the exterior Kerr spacetime. In this case, the analytic results for the first-order approximation are compared to the numerical integration of the exact system and the limitations of the first-order results are pointed out. Furthermore, we employ our analytic results to illustrate the gravitomagnetic clock effect for spinning particles.

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“…(48). This constitutes a generalization of previous results [18,19,34] that involved onlyŝ Ĵ 1. Imagine a spinning particle revolving around a Kerr source in accordance with Eqs.…”

Section: Gravitomagnetic Clock Effectsupporting

confidence: 85%

“…As noted in Ref. [34], a similar result has been obtained in the treatment of a Dirac particle in the Schwarzschild field [42 -45].…”

supporting

confidence: 79%

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Dynamics of extended spinning masses in a gravitational field

2006

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“…and obtain the differentiate between prograde and retrograde orbits and integrate from zero to 2π. The clock effect is the difference of theses two orbits [8], [9], [10]. The fourth group takes some elements of electromagnetism and does an analogy between Maxwell equations and Einstein linealized equations [11], [12], [13], [14], [15], [16], [17], [18], [19].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Mathisson-Papapetrou-Dixon Equations for Spinning Test Particles in a Kerr Metric

Velandia-Heredia¹,

Tejeiro-Sarmiento²

2018

Momento

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In this work we calculate some estimations of the gravitomagnetic clock effect, taking into consideration not only the rotating gravitational field of the central mass, but also the spin of the test particle, obtaining values for ∆t = t + − t − = 2.5212079035 × 10 −8 s. We use the formulation of Mathisson-Papapetrou-Dixon equations (MPD) for this problem in a Kerr metric. In order to compare our numerical results with previous works, we consider initially only the equatorial plane and also apply the Mathisson-Pirani supplementary spin condition for the spinning test particle. ResumenEn este trabajo nosotros calculamos algunas estimaciones del efecto reloj gravitomagnético, tomando en consideración no sólo el campo rotacional de la masa central, sino también el espín de la partícula de prueba, obteniendo IntroductionIn the last decades, important advances have been made in the study of the gravitomagnetic clock effect. Beginning with the seminal work by Cohen and Mashhoon [1]. In which they presented the influence of the gravitomagnetic field to the proper time of an arbitrary clock about a rotating massive body. In their paper, Cohen and Mashhoon, also showed the possibility of measuring this effect. In this work, we present a theoretical value for the gravitomagnetic clock effect of a spinning test particle orbiting around a rotating massive body. According with the literature, we find different complementary ways that study the phenomena in regard to the gravitomagnetism clock effect. The first way take two family of observers. The first is the family of static observer (or threading observers) with four-velocity m = M −1 ∂ t and world lines along the time coordinate lines. The second famili is the ZAMO's (or slicing observers) with four-velocity n = N −1 ∂ t − N φ ∂ φ and world lines orthogonal to the time coordinate hypersurfaces [2][3][4]. They obtain, in the threading point of view, the local spatial angular direction as

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“…H σ yields a gravitational acceleration à la Stern-Gerlach [2,3,16,28,62] whose effects on the orbital motion of a spinning particle were recently worked out in detail by [42] under certain simplifying assumptions about the orientation of J and the overall configuration of the system. For other studies concerning various consequences of the gravitational Stern-Gerlach effects on the orbital motion, see, e.g., [2,3,5,7,8,16,27,28,64]. Orbital effects of the spin-orbit term were derived by [2,3].…”

Section: Introductionmentioning

confidence: 99%

General relativistic spin-orbit and spin–spin effects on the motion of rotating particles in an external gravitational field

Iorio

2011

Gen Relativ Gravit

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We analytically compute the orbital effects induced on the motion of a spinning particle geodesically traveling around a central rotating body by the general relativistic two-body spin-spin and spin-orbit leading-order interactions. Concerning the spin-orbit term, we compute the long-term variations due to the particle's spin by finding secular precessions for the inclination I of the particle's orbit, its longitude of the ascending node Ω and the longitude of pericenter . Moreover, we generalize the well-known Lense-Thirring precessions to a generic orientation of the source's angular momentum by obtaining an entirely new effect represented by a secular precession of I , and additional secular precessions of Ω and as well. The spin-spin interaction is responsible of gravitational effects à la Stern-Gerlach consisting of secular precessions of I, Ω, and the mean anomaly M. Such results are obtained without resorting to any approximations either in the particle's eccentricity e or in its inclination I ; moreover, no preferred orientations of both the system's angular momenta are adopted. Their generality allows them to be applied to a variety of astronomical and astrophysical scenarios like, e.g., the Sun and its planets and the double pulsar PSR J0737-3039A/B. It turns out that the orbital precessions caused by the spin-spin and the spin-orbit perturbations due to the less massive body are below the current L. Iorio is a fellow of the Royal Astronomical Society (F. R. A. S.). L. Iorio123 720 L. Iorio measurability level, especially for the solar system and the Stern-Gerlach effects. Concerning the solar Lense-Thirring precessions, the slight misalignment of the solar equator with respect to the ecliptic reduces the gravitomagnetic node precession of Mercury down to a 0.08 mas per century level with respect to the standard value of 1 mas per century obtained by aligning the z axis with the Sun's angular momentum.The new inclination precession is as large as 0.06 mas per century, while the perihelion's rate remains substantially unchanged, amounting to −2 mas per century. Further studies may be devoted to the extrasolar planets which exhibit a rich variety of orbital and rotational configurations.

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Clock effect due to gravitational spin–orbit coupling

Cited by 11 publications

References 13 publications

Dynamics of extended spinning masses in a gravitational field

Dynamics of extended spinning masses in a gravitational field

Numerical Solution of Mathisson-Papapetrou-Dixon Equations for Spinning Test Particles in a Kerr Metric

General relativistic spin-orbit and spin–spin effects on the motion of rotating particles in an external gravitational field

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