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 postNewtonian 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 eects, 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.

/pdf/gravitational-radiation-from-post-newtonian-sources-and-g96j1cyq78.pdf

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries.

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 non-linear 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 35PN 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

/pdf/gravitational-radiation-from-postnewtonian-sources-and-3k5v1g98mj.pdf

Gravitational radiation from postNewtonian sources and inspiraling compact binaries

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 non-linear 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.

/pdf/gravitational-radiation-from-post-newtonian-sources-and-4vzs3h2415.pdf

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

The multipole expansion (in general relativity) of the gravitational field generated by a slowly-moving isolated source is constructed. We introduce some definitions for the source multipole moments, valid to all orders in a post-Newtonian expansion, and depending in a well defined way on the total stress-energy pseudo-tensor of the material and gravitational fields. The source moments parametrize the linearized approximation of the gravitational field exterior to the source, as computed by means of a specific post-Minkowskian algorithm defined in a previous work. Since the radiative multipole moments parametrizing the radiation field far from the source can be obtained as nonlinear functionals of the source moments, the present paper allows one to relate the radiation field far from a slowly-moving source to the stress-energy pseudo-tensor of the source. This should be useful when comparing theory with the future observations of gravitational radiation by the LIGO and VIRGO experiments.

/pdf/on-the-multipole-expansion-of-the-gravitational-field-3lrsb1smn6.pdf

On the multipole expansion of the gravitational field

The logic of gravitational field energy localisation for static or quasi-static fields is discussed. A particular form of localisation in the case of spherical symmetry is justified by physical considerations. This form coincides with that general form presented by Moller (1952) for the case of the Schwarzschild constant-matter-density fluid but differs when one considers other equations of state.

The localisation of energy in general relativity

In the framework of Landau and Lifshitz, the rate at which angular momentum is lost by a bounded matter distribution through the gravitational channel is shown to be\(dL^{\alpha \beta } /dt = - \oint\limits_S {( - g)\{ x^\alpha t^{\beta \gamma } - x^\beta t^{\alpha \gamma } \} n_\gamma dS} \), wheretαβ is the Landau-Lifshitz pseudotensor This flux is expressed in terms of the quadrupole and octupole moments of the source in Einstein’s linearized approximation Applied to a spinning rod, the angular-momentum loss is found to be consistent with the energy loss as computed by Eddington

Angular-momentum flux for gravitational radiation to octupole order

Bondi’s Newtonian inductive energy transfer by gravitation is rederived and new forms are presented to exhibit the lack of uniqueness of the Newtonian gravitational Poynting vector. Einstein’s power transfer theory is employed in a straightforward manner to deduce the energy transfer for weak fields in general relativity. The relativistic and classical expressions, developed in terms of the multipole moments of the matter distributions participating in the interaction, coincide in the limit asc→∞.

D. J. Booth

Papers

Angular-momentum flux for gravitational radiation to octupole order

General-relativistic and Newtonian gravitational energy transfer