Multipole expansions of gravitational radiation

Thorne, Kip S.

doi:10.1103/revmodphys.52.299

Cited by 1,476 publications

(2,366 citation statements)

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“…Between 1980 and 1992 important theoretical foundations in gravitational radiation and post-Newtonian (PN) theory were carried out by a number of researchers [30][31][32][33][34][35][36][37][38][39][40][41][42][43]. However, during those years, the analytical work on the two-body problem was considered mostly academic.…”

Section: Analytical Approximation Methodsmentioning

confidence: 99%

“…Using the conservation of the energy-momentum tensor at linear order in G, that is ∂ α T αβ = 0, and expanding the integral (6.3) in powers of v/c, one can obtain the gravitational field at linear order in G as a function of the derivatives of the source multipole moments [30]. As originally derived by Einstein [3] and then by Landau and Lifshitz, at lowest order in the wavegeneration formalism, the gravitational field in the transverse-traceless (TT) gauge and in a suitable radiative coordinate system X µ = (c T, X) reads ("far-field quadrupole formula")…”

Section: Post-newtonian Formalismmentioning

confidence: 99%

“…However, in their approach the formal application of the PN expansion leads to divergent integrals. Building on pioneering work by Bonnor et al [83,84] and Thorne [30], Blanchet and Damour [34,39,85] introduced a GW generation formalism in which the corrections to the leading quadrupolar formalism are obtained in a mathematically well-defined way. In this approach the wave-zone expansion, in which the external vacuum metric is expanded as a multipolar post-Minkowskian (MPM) series (i.e., a non-linear expansion in G), is matched to the near zone expansion, in which a PN expansion (i.e., a non-linear expansion in 1/c) is applied, the coefficients being in the form of a multipole expansion.…”

Section: Post-newtonian Formalismmentioning

confidence: 99%

“…The multipolar post-Minkowskian-post-Newtonian formalism: Early on Epstein and Wagoner [82], and Thorne [30] proposed a PN extension of the Landau-Lifshitz derivation and computed the O(v 2 /c 2 ) corrections to the quadrupole formula for binary systems. However, in their approach the formal application of the PN expansion leads to divergent integrals.…”

Section: Post-newtonian Formalismmentioning

confidence: 99%

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Sources of Gravitational Waves: Theory and Observations

Buonanno

Sathyaprakash²

2015

General Relativity and Gravitation

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Section: Analytical Approximation Methodsmentioning

confidence: 99%

Section: Post-newtonian Formalismmentioning

confidence: 99%

Section: Post-newtonian Formalismmentioning

confidence: 99%

Section: Post-newtonian Formalismmentioning

confidence: 99%

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Sources of Gravitational Waves: Theory and Observations

Buonanno

Sathyaprakash²

2015

General Relativity and Gravitation

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“…Outside of the planet, in vacuum, and in the harmonic gauge (10), the linearized Einstein equations for the field h are a homogeneous wave equation [46,51] …”

Section: A the Field Equationsmentioning

confidence: 99%

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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2013

Earthquakes

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Multipole expansions of gravitational radiation

Cited by 1,476 publications

References 54 publications

Sources of Gravitational Waves: Theory and Observations

Sources of Gravitational Waves: Theory and Observations

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

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