Gravitomagnetic effects in the propagation of electromagnetic waves in variable gravitational fields of arbitrary-moving and spinning bodies

Kopeikin, Sergei M.; Mashhoon, Bahram

doi:10.1103/physrevd.65.064025

Cited by 169 publications

(326 citation statements)

References 54 publications

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“…Our calculation method is general enough, and we do not need to assume that the parameters characterizing translational and rotational motion of the light-ray deflecting bodies are either constant or equal to zero, as it was postulated in [30] where the authors assumed thatx P 0, along withṽ P ã P 0 ands is a constant vector. We shall calculate relativistic deflection of light by a planetary axisymmetric gravitational field but ignore the relativistic effects caused by the gravimagnetic field due to the intrinsic rotation of the planet, since it is negligibly small and cannot be detected at the microarcsecond resolution [10]. We refer the reader to paper [5] where detailed estimates of the magnitude of the gravitational light deflection caused by various parameters of the solar system bodies are given in Table 1.…”

Section: A the Field Equationsmentioning

confidence: 99%

“…Indeed, Einstein's theory of general relativity is formulated in a covariant tensor form while the wave equation (11) is valid in a particular harmonic gauge only. First of all, we notice that the harmonic gauge is not reduced to a single coordinate system but admits a whole class of both global and local harmonic coordinates related to each other by coordinate transformations which do not violate the harmonic gauge condition (10). The class of the global coordinates consists of the reference frames which are moving with respect to each other with constant velocities in the asymptotically flat space-time.…”

Section: A the Field Equationsmentioning

confidence: 99%

“…(27) by a factor of d=r 1 v P =c 2 [2,9] that also amounts to j i j 1 as, and can be ignored. In cases when i may be important, for example, in studying the refraction of light by gravitational waves [2,62] or in cosmological gravitational lensing where r 0 Þ 0 and r 1 is comparable with r 0 , this term is solved in our papers [9,10,61].…”

Section: B the Null-cone Integration Techniquementioning

confidence: 99%

“…We shall omit in this paper the relativistic effects of the planet's spin, and consider only the mass monopole, dipole, and quadrupole terms in the multipolar expansion of the gravitational field. Relativistic effects caused by the spin and higher-order mass multipoles are discussed in [10,34,61,62].…”

Section: B the Gravitational Multipolesmentioning

confidence: 99%

“…Moreover, in the case of a photon propagating near the planet the interaction between the gravitational field and the photon can no longer be considered static, because the planet moves around the Sun as the photon traverses through the solar system [9,10]. The optical interferometer designed for the space astrometric mission SIM [11] is capable of observing optical sources fairly close in the sky projection to planetary limbs with a microarcsecond accuracy.…”

Section: Introductionmentioning

confidence: 99%

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Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers

2007

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General-relativistic deflection of light by mass, dipole, and quadrupole moments of the gravitational field of a moving massive planet in the solar system is derived in the approximation of the linearized Einstein equations. All terms of order 1 as are taken into account, parametrized, and classified in accordance with their physical origin. The monopolar light-ray deflection, modulated by the radial Doppler effect, is associated with the total mass and radial velocity of the gravitating body. It displaces the apparent positions of stars in the sky plane radially away from the origin of the celestial coordinates associated with the planet. The dipolar deflection of light is due to a translational mismatch of the center of mass of the planet and the origin of the planetary coordinates caused by the inaccuracy of planetary ephemeris. It can also originate from the difference between the null cone for light and that for gravity that is not allowed in general relativity but can exist in some of the alternative theories of gravity. The dipolar gravity field pulls the apparent position of a star in the plane of the sky in both radial and orthoradial directions with respect to the origin of the coordinates. The quadrupolar deflection of light is caused by the physical oblateness, J 2 , of the planet, but in any practical experiment it will have an admixture of the translation-dependent quadrupole due to inaccuracy of planetary ephemeris. This leads to a bias in the estimated value of J 2 that should be minimized by applying an iterative data reduction method designed to disentangle the different multipole moments and to fit out the translation-dependent dipolar and quadrupolar components of light deflection. The method of microarcsecond interferometric astrometry has the potential of greatly improving the planetary ephemerides, getting unbiased measurements of planetary quadrupoles, and of thoroughly testing the null-cone structure of the gravitational field and the speed of its propagation in the near-zone of the solar system. We calculate the instantaneous patterns of the light-ray deflections caused by the monopole, the dipole, and the quadrupole moments, and derive equations describing apparent motion of the deflected position of the star in the sky plane as the impact parameter of the light ray with respect to the planet changes due to its orbital motion. We discuss the observational capabilities of the near-future optical (SIM) and radio (SKA) interferometers for detecting the Doppler modulation of the radial deflection, and the dipolar and quadrupolar light-ray bendings by Jupiter and Saturn.

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Section: A the Field Equationsmentioning

confidence: 99%

Section: A the Field Equationsmentioning

confidence: 99%