Post-Newtonian Gravitational Radiation

Blanchet, Luc

doi:10.1007/3-540-46580-4_3

Cited by 12 publications

(21 citation statements)

References 84 publications

(266 reference statements)

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“…In the (t, x) coordinates, projection of the conservation equation along t a (where, as usual, t a ∂ a := ∂/∂t) andq b a yield, respectively, 12) where the matter density and pressure are defined as usual via 13) and whereD a is the derivative operator compatible with the flat spatial metricq ab . (In the last equation, there is no sum overī.)…”

Section: B Expressing the Approximate Solutions In Terms Of Quadrupomentioning

confidence: 99%

“…Today, observational evidence yields a confirmation of the existence of gravitational quadrupolar radiation to an accuracy of 3 parts in 10 3 [8]. Einstein's calculations and its subsequent refinements and generalizations (due to Eddington [9], Landau and Lifshitz [10], Fock [11], Blanchet and Damour [12] and others), as well as the Bondi-Sachs framework in full general relativity [5,6], use field equations with a vanishing cosmological constant, Λ. On the other hand, by now there is strong evidence from independent observations that the dominant contribution to the energy density of the universe is best modeled by a positive cosmological constant Λ [13,14].…”

Section: Introductionmentioning

confidence: 99%

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Asymptotics with a positive cosmological constant. III. The quadrupole formula

2015

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Almost a century ago, Einstein used a weak field approximation around Minkowski space-time to calculate the energy carried away by gravitational waves emitted by a time changing mass-quadrupole. However, by now there is strong observational evidence for a positive cosmological constant, Λ. To incorporate this fact, Einstein's celebrated derivation is generalized by replacing Minkowski space-time with de Sitter space-time. The investigation is motivated by the fact that, because of the significant differences between the asymptotic structures of Minkowski and de Sitter space-times, many of the standard techniques, including the standard 1/r expansions, can not be used for Λ > 0. Furthermore since, e.g., the energy carried by gravitational waves is always positive in Minkowski space-time but can be arbitrarily negative in de Sitter space-time irrespective of how small Λ is, the limit Λ → 0 can fail to be continuous. Therefore, a priori it is not clear that a small Λ would introduce only negligible corrections to Einstein's formula. We show that, while even a tiny cosmological constant does introduce qualitatively new features, in the end, corrections to Einstein's formula are negligible for astrophysical sources currently under consideration by gravitational wave observatories.

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Section: B Expressing the Approximate Solutions In Terms Of Quadrupomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Asymptotics with a positive cosmological constant. III. The quadrupole formula

2015

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“…This has been extensively used in a number of problems, in particular, in weak-field approximations dealing with equations of motion and gravitational radiation (see, e.g., [54]), but not in cosmology. The gauge conditions (4.…”

Section: B Gauge Conditions On the Time Slicingmentioning

confidence: 99%

Cosmological perturbation theory, instantaneous gauges, and local inertial frames

2007

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Linear perturbations of Friedmann-Robertson-Walker universes with any curvature and cosmological constant are studied in a general gauge without decomposition into harmonics. Desirable gauges are selected as those which embody best Mach's principle: in these gauges local inertial frames can be determined instantaneously via the perturbed Einstein field equations from the distributions of energy and momentum in the universe. The inertial frames are identified by their 'accelerations and rotations' with respect to the cosmological frames associated with the 'Machian gauges'. In closed spherical universes, integral gauge conditions are imposed to eliminate motions generated by the conformal Killing vectors. The meaning of Traschen's integral constraint vectors is thus elucidated. For all three types of FRW universes the Machian gauges admit much less residual freedom than the synchronous or generalized harmonic gauge. Mach's principle is best exhibited in the Machian gauges in closed spherical universes. Independent of any Machian motivation the general perturbation equations and discussion of gauges are useful for cosmological perturbation theory.

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“…For reviews on analytic approximations and applications to the motion and the gravitational wave-generation see Refs. [143, 53, 54, 144, 150, 8, 13]. …”

Section: Introductionmentioning

confidence: 99%

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

Blanchet

2002

Living Rev. Relativ.

Self Cite

461

764

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The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the post-Newtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many nonlinear multipole interactions, among them those associated with the tails (and tails-of-tails of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail effects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary’s orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.

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Post-Newtonian Gravitational Radiation

Cited by 12 publications

References 84 publications

Asymptotics with a positive cosmological constant. III. The quadrupole formula

Asymptotics with a positive cosmological constant. III. The quadrupole formula

Cosmological perturbation theory, instantaneous gauges, and local inertial frames

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

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